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<h2>HL Paper 3</h2><div class="specification">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math> is a simple, connected, planar graph with <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math> vertices and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math> edges.</p>
</div>
<div class="specification">
<p>The complement of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math> has <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>'</mo></math> edges.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the maximum possible value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>'</mo></math> in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that the complement of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math> is also planar and connected, find the possible values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi></math> is a simple graph with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math> vertices and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math> edges.</p>
<p>Given that both <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi></math> and its complement are planar and connected, find the maximum possible value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Christine and her friends live in Winnipeg, Canada. The weighted graph shows the location of their houses and the time, in minutes, to travel between each house.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>Christine’s house is located at vertex <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use Dijkstra’s algorithm to find the shortest time to travel from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>F</mtext></math>, clearly showing how the algorithm has been applied.</p>
<div class="marks">[6]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence write down the shortest path from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>F</mtext></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A new road is constructed that allows Christine to travel from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>H</mtext></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> minutes. If Christine starts from home and uses this new road her minimum travel time to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> is reduced, but her minimum travel time to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>F</mtext></math> remains the same.</p>
<p>Find the possible values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>This question explores how graph algorithms can be applied to a graph with an unknown edge weight.</strong></p>
<p><br>Graph <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math> is shown in the following diagram. The vertices of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math> represent tourist attractions in a city. The weight of each edge represents the travel time, to the nearest minute, between two attractions. The route between <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>F</mtext></math> is currently being resurfaced and this has led to a variable travel time. For this reason, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AF</mtext></math> has an unknown travel time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> minutes, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>∈</mo><msup><mi mathvariant="normal">ℤ</mi><mo>+</mo></msup></math>.</p>
<p style="text-align: center;"><img 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sLhkTMl0yWtyb2yZG/t6l/JRjfA4WPYwwCvlL1L7pUmTZo0eKVNKZEz2qd0sP5Gt27dtC1iJdCTh3/VvHnzuBre4RAsDTcY8Fbgs+BvJsGxh3B4jsvWP74rFfIXee6tfQ0arUSDm3f48OHqe+SgN1bhagU8n28X16k8KauqUU1J9VVzSJzZv5BHB9wirbTP6cDfSE9P17aIFcB9j84SImyAISB4ecm8/3ft2hVRJ41RR5jA47A6NWVOJTtrhJKb5VDEMU0pPl2jHUk8LpdL6dWrl7J582Ztjx2oUarKPlK8oqFt16JehwDn39ugwGfTtojZ2blzpzJ58mT1vsf9f/bsWe1I8hk7dqzijWa1rfDQ70f8JIGxgTn+pZRMGSKLuq6QV1qvkp/lbJdBrvdk1dBrExpu+Rrgs2bN4kyv8q2Ur86VrLLH5fCivvUiDvg+GPPG8AUxJ4EM71TPeqCb3dE0cSgYxDxYyPAiDbH+UNWZT2Sz6zYZP+BG6dB/qDzqOCirVxbLEY92PAHoBjjWAoABTtHw4jkmO9/8POAwFfyN22+/XdsiZsLf8Ma0ILrhnWrCScMNxrBhw1TxoNcRGIsLh7eX+/ZL8lrOUOl/9aUirW6RAY9miGzZJDuPfKt9Jn74G+CBpjewK54jf5M3D/SRAT0bmpT0N8yHr+GNZX51w7t79+7aJ1KP/2y4kYAsL0z9Q68jMNYWjupP5M+vXSLzxvxC6+VeKZkPPiJZsl5mOv8WV5PcjgZ4+HwrR3ZukgOP9peererfcmiA0FPl+TIHuM9RsOdreGM4x4jXL9w03GAgZZ5RRxDgcViTGuV08TTF4f2K+JoNXnE0ye1pgEdAzSHFmf0LJb/4pLbjIrqRSowNrhOM5iFDhqTc8A6HsrIy9W+NFXzXZcuWaVtEx7oRh6dc3l60XR4tPlmbClr3OidlzmEiFVtkc2lsPQn0RND7wiyeGOflHEuBUYepLvxveTCz4TAV/Q3jgqFXzB+FwkyY3liSFb14pLcafXqcgwcPxqVWSo86sNwBuYhFheOMHF5TIDOPPiAP/rKdtk/ncuky6GHJlb2yeO5zUlQe3YAV5thBuI6xeRrgoaiU/X9+V+TRQXJbi4a3G/0N44EOkW544/rAuzCK4R0u6MwFmw03EnSvY+nSpdoeooKww1pUKaUFWT7DUuMVl/s77ZgXt0vJrTuGVycl1/WZdrBxEKIjdMXQVKT54bbkdLGS7ximOMvOaTsuwvoNY4HrgXsb1wQ/jx8/rh0xF3hG43lf4ffhecfwF6mFkxxGAMJV3QicM2eO4cN1o8P6DWMAw/uVV15Rl2TF/X3vvfeaeg413FdIUEGVerxABIYqdN6rtVg7qyoK9HFdDD/hBsQ2wI3ToUMHmTBhgnrzUDRih/6GR6rLN8uSUTdr83gNkCmFe6QigTVGvuD+hn8Bnw7XAY0tUsjNPvEm7qtYsqkCAa8DwgqRJV7UuIOoIDTv3LmzGubi1b59e6VHjx7Kk08+qWaUmDV0NyrIerFz+F9zwqXkOdKVXOcBpQrTtBxao+Q6HEpWwW7vdmLAsAsyhXDu8UK2lNXAsFIinlWcN2YA1kLh8GHEiBF1ouH76t27t+HTD80G/Y1zSplzmCKdCpTSOgtO2yeBPaFYwPkuLCxUG1U0flYVbAhGPNJwA0Gv4yIcqvIhWJWot1fGoak4g+kgMJ+RfTkpB7fv097rXC6dew+UbPlUyk5Ua/tiA74cKrwxZxPmXtq0aZM61GrVgkssBNa/f39tK77oGVbwg+wOhYOkBPobP5TW7VuLnD0lp8/6mxqV8kVlrbcWLXqFN2oZsB6FXuFtdv+iMZCG27t3b20r/tDrqIXC4cPPf/5z7V19Bg8erL0j8YL1G1dKzwHZ4qhYI3Pnb5Dyaq94eCqk9C/b5YC0lvato4twfQ1v9LxheEM8rC4YAIksiAa6du2q7Yk/jDo0tCEr4gXjo9dcc009f6Njx440xeMM/Q2d00qZa5qSpd5rDiUrf56SH8WaMbrhjfF3JHFY0fAOh2RNX0Ovg3UcDVixYoWUlJRImzZt5LbbbpOHH37YFr21ZML6jSCcKZEp3UbKnt9tkHefzpQW2u5goMIbvhymxMjKyhKvaNh6skh4Ofj+yZj6x/Z1Hap8EBW9J4EeMUkcqEpGD5n4UHVAceamK5L1nFLqt3KiP+jp+lZ4836tBc9uskYHooo6ao4prjzvNVYjzNooM9t5SInPVKvJhR6HD1jBDD03RhiJhf6GL2ekvGS1TBmcLTPlcdn9+kTJCDCnF8D8aPAuRo4cqRre3sbLFoZ3OCB7DOckWXPGRe51eKR6f5Es+zRPvB0DdNi9L7dszutmTqO5Vj8IsGpBlJGgv6HjM6daVr7i3FCquIN0PXFP+hbsobdL6pOK6c8jijrUaCNLyXMdM2WE4Q+fYA1c/EQVDpGLJMvANDtolHTDG+eLHZrQICkgFZOOhnc/+64NlK7kFryhFJed1o6ZEw5Vabz99ttc6jUJsH4jNDC8YfJiSvPDhw/XLclqpinNk00y0nCDgeuCmo7QdR1NpVXfBeJWzou79Fnpc3K19Ot6h4xafVDiU+aZAjQBsTX68AmHABIPojo7pzEGA+dk/vz56n1IwzsyUh3FRv7/n1YOOfO8Ecg9SkHp19o+c8GIw8t7770n3oeV04okGPSmub54fZCarBve3bp1o+EdBYhiEzXNSDiEF3X40kq6jZ4s87L3yUt/PSrfa3vNhO2FA2EuhgZQbUsSC+enqgX3nF7hjSVZvVFYXYU3Oy+RgzqWm266SdtKDbivcS3Dpmk7ua57mrZhPmwvHHoKLpd+TTx29zcgGPqSrIi8Zs+eXbckKwUjOpKdhhsMXMOTJ0+qHYKw8Hwpxz7qII/f1UmaabvMhO2FQ+/xkcRj1/oN3fBu3ry5uN3uOsO7e/fu2idItCRyNtxICRp1eCpk7ztF8s7eClGns6w+LEXTnpbX7p4mj2e0Vj9iNmwtHPqYJDNWEo8d/Q3cXwsWLJCBAweq219pM9TS44kfiZ4NNxL0dqRh1OGR07tXyv090+QHWOlx8B+kcsBzYU0rY1RsPVcVHmoYkhhbJonFTvNT4buuWbNGPv74Y7W6GFNxcygq/mDoD1EcEgqMcn5x7RF1YAjSytg24kAPeMaMGepDTRKP1f0NNGJYq143vEePHq0Oo9DwThxlZWXq8JCRzm/wqMNa2FY4mIKbXKzqb6ADohve+I6+hjdJLDt37jSMv+FLxBlWJsSWwsEU3ORiRX9DN7yxJCsMb4gHDe/kAqFOdRpuIOwQddhSOJiCm1ysVL8BwxsFezC8W7VqVWd4815KLkjDBUY971aPOmwpHLigTMFNHlbwN9B7HDdunCoa+C4o2MPcZqzwTg3/+Mc/DDlMpWP1qMN2wsEU3ORjVn8jkOEN/4KGd+rBPYUVOo2MlaMO26XjMgU3ucALgA9gptsMfzOSJ+BhcElW42HENNxgoNMBAbFaR9VWEQcaBKbgJhcz+RsYN9cN7zNnztQZ3hQNY4E0XIi5GaI+q0YdthKObdu2MQU3yZjB39ANb0ShmPeIhrexQRquWTp/VvU6bCUcCxcuZApukjGyv4GHGfcDRANGqz5DLQ1vY4N7KjMzU9syPqjtsVrUYRvhQCPBFNzkYsT6DYyPYwgKgoFpQTCUAMM7OzubkagJwHAi6mbM9ByjtgfPgJWiDtsIBxoJpuAmFyP5GxAxrNuACu9du3ap3sWqVauYXWcykIZrxiWe4clYKeqwhXBgDBsTzrGRSC5G8Ddw7X0N702bNtHwNjFmSMMNBO43K0UdthAO5OJjllKSXFLpb3z00Ud1S7L6Gt70L8wLhhnRa+/Ro4e2x1xYKeqwfB2HXkeAhoONRvLQc+2TfXuhR6c/nBMmTJA777yT3oVFQGdg+fLl6hCjWdETMeCpmRnLRxx6Ci5FoxEqimQUFpnxfY0qkoogxzov2RtykX19yutkoBveyLSBGU/D25qYKQ03GIg6Zs6cqd6zZsbywoEUXLOre1JwDJVC5ZyUOYd5N4aJs+ycKIVDxVF37KQU52fUHTvydEbItZI/+eSThPsbiCbhX8DwPnz4cN2SrPSyrInZ0nADAZ8D2Z1YudDMWFo4MGxx66230ggNm2bSsjUisyuldUt/WbhcrriqpfdnoGMN2bFjR8L8DV/DG8Dwnj59Oq+zhTFjGm4wEHWgQ2vmqMPSwoEUXExMR5ILHohXXnkl7g25v+GNuYpoeNsDs6bhBsIKUYdlhYMpuKkjnv4GRAiRIwr2UIGLWhy9wpv+hX0waxpuMMwedVhWOJiCGwsrJSftknpmeJMmLaXn5G3a8dDEw9/AA6UvyepreKMjQMGwF7gXzJyGGwizRx2WFA6Ypk8++aR6YUg0jBeX+zs1lfbiq0pKC8I7n7H4G7rhjVRejGnT8CZmmg03EswcdVhSOJiCmzrwEETjb2BoEWulYElWoBfs0fCOkOpyKSlaJVPuullGFR3XdvpyQSr2LJdRaYgi0+SuKa/J3ooL2jFjYoU03ECYOeqwpHAwBTd1ROpvwL/QDW8ssAX/goZ3tHwpJXNHSL+cx2TxtkC9WI9U710uI372Z7l67QmpqflQnvnBWhk88z353KN9xIBYIQ03GGaNOiwnHEzBjYXvparylPfnKams8i/v+1ZOn6zy/gx07CLh+Bt4SHTDG2PXMLz37NlDwztm2knfRaVSU+aUgN0mT7m8Nb1AyvKnyNS+V0vTpldL1uiH5ObVC2Tpti+1DxkLDF1aJQ03EGaNOiwnHEzBjRK1OvyH0nXMeu/GehnT9Yd+leNXSb/Fe+uOBascD+VvoBHwNbyRJaUb3iR+NG3ZWtpr733xHPmbvLmludz9sxuklbavaedfyEPZbnlt8ydyRttnJEpLSy2ThhsMM0YdlhIOpuDGgFod7muGe1/1KsfrH/OvHEcE8cYbb6j+RocOHbS9teiGNwr2fA1vrFNAkoVHqk8ckQPSQW6+to22z0vTH0nr9s2l4qNj8oUBh6sgHFZKww2EGaMOYwpH3dxIN8uYon96b3kfQ6/zEtkbZKSEKbjJB72k++67Tx544AEZPny4/OhHP1IfAlT6QsjhX9DwNgIe+abyVG0EGYijp6TKgMIxY8YMS6XhBsNsUYcxhUPt4X4tpQXXyuqVW2T/ntXywsE+stzt7e0eeVoyAsx4wRTc1IAH+91335WTJ0+q2998843qV/Tt21cVDfgdNLxNQKcrpaXBWgPMFGDFNNxAoDMFz88sUYeBh6paS8YjeZK75TEZvPLHMml0urTQjgSCKbip4fnnn9fe1ee//uu/ZPXq1TS8DUMz+Ul6pmRLlZw8/a22z8v3/yOffnBUHN2vk/YGaw2QaIFp8e3C448/bpqow8DC4eUnN0mf7HS5+55ecnUjfymWBWUKrnFAAR88Db3yHL0pRCD6Cya5/oI/gmEt/UUSQyAj3PPpx/L+0Qx5dMAtdYa5UcC9keoVJJMJOr1IBDBD1GHshZw8h2X1oL4ys/taObyob9AbGw0PsqnMvMCL2UCvCDf4mDFjpLKyUtt7EeTd7969W9uqnd0UkxIC/Pz000/V9wBTouu/4+uvv1YNdh2k6uqeSOvWrdVaD52f/vSnqkAB/LRqymakeMpXy6CuM0WcJbIxr5tP7/CCfF70O+n1xDmZV/K85F3jlqK5v5EnvhwvH64a2mjnLJlg6BneGIY97YT+vTG8a+RI3cDCgZu8QJbu/oe89tq1svbwPOnbKvCdjR4sGhhmUyUeXTAQUsNPuvfee9Vz7y8eWG88HllTvhEIfJR//etf2pbIrl27tHe1n0OKrw7Gxtu0qc0e6tixozqbro5vunC7du0sNLxZLXuXDK4/p1inAik97OsLnpHyooUyPudZ2SYOycp/UVY+c790aWGswQckuiCjCtPl2w1kIOJ+xTCvUTGocHik+vAfZe7GrvLMmGqZ2+0l6brtFRlw0Clb038to7pcrn2utieLE2x0hTY7/oKBhhmRAB7wF154Qe666y618b722mvVOppU9/59BefYsWNSXV2tvsfPgwcPqu8BvLEPP/xQ25J6Ve++gtOiRQu57rrr1PcAKce83xIHpp9BvY8dO4N61IF1ZozaqTGccOhh9oW6ntApKZkyUPq99m/y3IaF8ptMRz1jBurcqlUryxcJpRKIA5a79BUMoN/gqMuwQootxPH48YvzO/kKDOpPPvvsM21L6tY1B7169aqXzYeIBkIDfvKTn8hVV12lvgdWOE/JAL4Y0rftmuyCdg0gG9GIGNvjaAQ86BjbtvMNlkjgHaGBRGPnKxg6GCJEI2l30YaAfvnlxSk7fAUnXP8G+BrBvoJjN/8GabjLly+3tWeJewrJJUZt20wtHMi6wINpx3HQRNKYYABEIStWrJB169ZxyCZKQiUMhOvfhEoYMKt/gwxJYPcOiZGjDlMLB1I8MXVFoIaNRE44ggGsNkRlNsJNGAjXvwFGShjgc12LkaMO0wqH3shhkjwSG+EKhg6HqMyHv38TKmEA94JOKP8mEQkDeqfEbmm4wTBq1GFa4WAKbuxEKhiAQ1T2IpR/E0nCQDD/Bvjed3ZOww2EUaMOUwoHU3BjIxrBAByiIuESbcHnjTfeqM6Ge/XVV7PgUyO8qON7qSh6QtJyVmrb/mRLvnOc/OLWO2RwRv3M1GgwpXAwBTc6ohUMHQ5RkUSDNFwMU11xxRVRF3z6C46R/JtoiCjqOFMiU7r1k8V3u8StL4vgqZC9G/4oS5+YLK9WeJ9f5zpZnhd67r/GMJ1wmCkF11OxR1574RkZvXhL7Y6sfFmz5LfyaBwUPxJiFQzAISqSaGJJw7V6wScmE4VwosPscDjUpZYDP8fHpWjUXZIjiy8Kh4an4n2ZOWKUPLuthxSUrpWnM1prRyLHdMJhmhRczz+laNy9kvPpYHGtnCpDvdf48OqnpO+YKplX9qrk+VS/J4p4CAbgEBVJBslOww2VMBBtwae/4MTjecHfecstt8iRI0e0PaJ6RFg4DcsX1Ce4cHgbJW9AMlO69XtWJL845Px/jWE64TBNqt73e2VJt57yXI7PBcICVWkLpH3xJlnUt536sUSgCwaIx7niEBVJBmZ5tkMlDCSi4HPevHnyzDPPaFv1aTjyEko4vOhDWTJNikPM/9cYphIOvUE0RQquHnFs7COuD5+ToVdfWjudStYRmRLDBQuFr2AgBI9HxhmHqEgy0KNaK6fhhpsw4O/fYP63f/7zn9pWfcrKyvyEthHh0Dq0k4+OF5f7RRnqCLAqXjhAOMyCtzFUdu7cqW2ZgKoDijM3S8l1HlCqak4oxdOG1b7XDscLnBNvb0Z9xfP8eHszijcsV7zhvLaHkMSwefNmZf78+doW8cUrqOjcN3h5BUXxCof2KZ3PFFduJ0VyXYpb21OP08VKvsP77zsVKKXfafuiIJkebUxArWFsmWr94RZdZNDEh6Tdm+Olyw8GSmHn/xNzNoMviDAQ3iPKQISBSCyedS2YCRdruNtpniSSGlC7gdlwSUOwlj8yxfy55JJLVNM+fDxypnSrvFYh4sjpITdEGWwA0wgHGkXkMZtnuOSCVJQ8KyOmnJMRrmLZu/txkZk3S8u75khJxQXtM9GRaMEAGKLCGK2R1wQg1gFr16OGgzQEHbdmzZrJj3/8Y22PyPXXXy9/+ctfImoPPRXFsnDuGqmQe+R3D/aIbcVHLfIwNGfPnlVDMwydmAY1JHQo2c5DSo26o0apOrRGya23LzISNSTlD4amcL6DDVHVuLco07IcSqeCUiWGaJcQFQy3jB07VtsivuAZxHDx/v371ZfL5VKH9dAmBkQfivIdqqpxK6WuAm/bgyGubGVa8Ymo2h9fTCEcOFlmG/+sKXMq2eIvErXjj5E2uMkSDB08xDjnAak5prjy0lVhoXCQeFBYWKi+SH100Qjvmf9OcbvGq89l4Fe2ku90KcVlp7XPx4YphAMNZkMTyODUHFKc2Q5FHHmK8xAu1nnFXTxbyZJ7lILSr2s/0wjJFgwAwQje+zuvnHBNVDplZSm/8N6MFA4SD3C/me75TjCIKPDcB+3ApRjDCwfCM5xAM1Lj3q2syc++qPpZ+cqaUnejYWIqBAOEHqLShtqyn1NKy9YruRQOEgf0zD1yEYgGxHTZsmXaHuNheHP89ddfrzctgJlo6siUUYs2Q5xrX39dJKNCTDeSDNM7FHPmzBFvDydwFlV1qbz0m/+UPr8fIxktTZNTQQzOoUOH1HueXATTi2DeLaMuGwsM3QKgKMh0KbhRkGrBAJjKBQTOoqqUvS+9KqemPCOju8WUi0FIPTDDdc+ePbUtgglc//u//1vtxBkZQwsHog1Mc2HVimUjCAZAjUxOTo7MmjVL2+ML0oqXy1LJlel9rzZP/jYxBbjnKRy1oPO2detWWbp0qfHbPHXAyoBgnA9jn6ZKwQ2TVHkYwQiZRaVXouo+TYPXeMXlptNBIgeGuFn9y3iDdsBMszQYdq4qFKBBfTHpmVVAhIHoAiDCSEV04Q96ORs3boxsKmt1ssYc+aCgVA4/nSExFKASG5Ps2XCNCuam6tq1qzpTr1lmaTDsyAMm1hsxYoS2ZW6MMiTlT+ghKkISy44dO9Tpwu0MnkGsreGNOEw1tY8hhQMLuoDu3burP82KUQVDJ2QWFSEJBIkvmHLc7M94LGCdDSSjYNp0I7UL4WDIoSqs/9C/f3/Jzs7W9pgLIw5J+RPVEBUhcQLPCDKqDL8gW4KAaEyaNEluvfVWQ6fdBsNwwqHPy4+bymzZVGYQDIDwGLNqmmlMlViLBQsWqNlUZu0cxsq4ceNMKxrAcMKBPGZgphNqFsHQwU07bNgw2z60JPVkZmbKpk2b/Favswdo4z7++GNzpN0GwVAeB8I3ZFqYxRQ3uocRCAxRoSqVokFSBbKI0tLSbCkaaN/MLhrAUBGHWVJwzRZh6OCBRQaHXXt6xBjYNQ0X7cZTTz2ldt7MPkRsqIjD6Cm4ZowwdBDNIekAGRwUDZJK7JiGayXRAIaJOJCCO3v2bLUxNhroqSN1ED/NFGH4gl7ewYMHLVVQScwHkl/atm2rTvppF5CMgrTbl19+2TLpx4YRDiOm4FpBMACHqIhRQM/bTmm4umhgxluzth+BMIRwGC0F1yqCATBEhcXuJ0yYQEOcpBw7peHqtRp33nmn5fwcQwiHUVJwrSQYOhyiIkbCLmm4Zi/wa4yUCwdOcJ8+fVJ6M1lRMAC+D4eoiFHA/YghaSP6mPEGkVVlZaVlO2wpz6pChkVWVlZKGjb9RsZryJAhpsqSagxmURGjsWvXriALhVkLsyzGFAspF45UpOBaWTB01q9fL126dKGvQQyDHdJwUYuG4WGzF/g1RkqHqpIduuL/s+KQFMDNunz5ctmzZ4889NBDcvjwYSkpKWG0QQwBIuDmzZtbOg3XarUaoUipcCQrw8LKggEwHIUezsmTJ7U9tXASQ2IUrJ6Gi7bFbIsxxULKhqqQgotIA6lqiQIX0+pDUjiPK1eubCAaYNGiRdo7QlLL/v37Lbu2uFkXY4qFlAnHe++9p+Y2J2IcUBcMXMzbb79d1q1bZznBAAj/S0tL1Rs3EMH2E5JsMJRqReHAM2jWxZhiISXCgZONzAPM+xRP/AUDoTEuqtlNKpwvfDfdeMN3RD48xowxBNeyZUvtk/XBcUJSDTowVpwNF88lajXQAbZbEkpKhGPfvn1qCm68wjqrCEYogcDEioguWrRooWahwYCDPfXWW2+p59Kfyy67TI4dO6b+PkJSCRI2MJ2Q1bBygV9jpMQcR6QRD5MajSJ63Nu2bZOpU6fKoEGDTCEWEAiYaGjYv/jiC7WyG9/hww8/VM9Lx44d1R5aenq6tGvXrtGeGnp0uIkPHDigfhYPKjKsOnfuLDNnzlRvbCzcZOX0QGJcsHDYxIkTLbW+uBUWY4qFpAuHHh3EkoJrFsGIt0A0BgTk7Nmz6rKw+vmAeb5w4UL1nKGKFbUdhCQLPAOImHFfWqWBxWgAalLsKhog6cKBFNxu3bpFVUFqVMFItkBEA4a/GH2QZIM03HfeeccyU2/YqVYjFEkVDn0u/kh7H0YRDDMIRCgYfZBkgyEdq8xggDWDHnvsMduLBkiqcCDEO3PmTNhmUqoEw+wC0RiMPkiyQHKHFRpaDANjlMRq62pES9KEA40xZsEN5yZKlmBYQiA8FbL33ffkrRdmyeJtFbX7svLF+cyvZIDsk9IbH5Qhjma1+33Ad8dDAK/JSiuTEeOAxhadk2RNKZQoKBoNSZpwhDPWmSjBsGoE4al4X2aOGCXPlt0tBS9OkkfuzxBHU+zfI6+98IyMXnxBCkrflaczWmj/oiF6+I1MN4zdMvog8QKdRLfbHfYIgxFB22HVxZhiIWnCESoFN16CYVWBCEj1QVk9cbiMeT9TnCXPS163VtoBDc8/pWjcb+XTCa+FFA7A6IMkArOn4eqiYddajZBAOBJNWVmZMmTIEG3rItjvbdCVXr16KS6XSzl79qx2JDT4HP7t5s2blcLCwrrfga+D98uWLVN/Hz7z1Vdfaf8qHpxXTrgmKg7v/4P/S31lO5WyGu1w0rj4dzjyi5XT2t761ChVpS8rBcUnte3G2b9/v3oe58+fH/a1ICQQuH/wfJj5PkI7MnbsWG2L+JKwiAMZPDDD//73v6srYQ0ePLgu1As3wjBcBFG9R5YMflZkyR+8vfjW2s5UcFyKRt0lOa+2lvziTbKobzttf+ww+iDxwOxpuHYv8GsUVT7iDHqu+NW+r+uuu07Zvn17wAgjdRFEJNT28jvluZQTSY8w/PiuVCnohPOapRSUVmk7dT5TXLmd6p17yXUpbu1ouOAaIkpE9JG6c06Sgzc6Lfur4nLmK1kyXnG5v9P2+3Jece9+Ucl14J5yKFn5ryql7vPasYbgmcXzbEbwd6P9YdQdnIQIR2ZmZv2GS3u1adNGvaHWrVun/oQo6MeMIxBBOF2s5KsPjSiO3AJlfXGZ4t9kJ42aQ4oz2+H9Wzopua7PtJ2+YJjqOW8jEGooq3Hw4EDI8RCZtREgYeBzb0tA4dDvp2xlWvEJpabmhFI8LVtxhOhE4Z45fvy4tmUedu7cadq/PZnEXTjQ4Hfu3Fm7CRu+DC8QjVDjLlU2qD0zCMga5VBVKsKPc0qZc5h6PoM+vG6Xkus93qmgVAnUf4wEXCdEH7h2jD6sin5PBRAOraPi2wmpKXMq2ZKh5Afw0NDoBvI0jQ7+bjxTuN9JaBIyO251dbX2riGY2RUZCsiLRkWp2TKbmjoyZEjes/LuoTVy9/vT5NcvlUrwb5soLpfOAx6WPIdIxeqVsnzb5+LRjiQCXCesaQIvaeDAgWoBIbEazaRl68DPoufI3+TNLc3l7p/dIHruXtPOv5CHst3y2uZP5Iy2T8eMs+HqtRpYjIkzKjRO3IUDQnDDDTdoW/UZMGCAzJ49W60mhfmEGgJz0lRadHtIZszrLdte+n9S9r22O4k0vfp++X3JGsl1bJFn+w2UXy0pkr0VF7SjZ6T8P0vlM20rHsAgRHLD2rVrZcWKFepElUiAIFbHI9UnjsgB6SA3X9tG2+el6Y+kdfvmUvHRMfnCr9eyceNG6d27t7ZlfJAQAtGw22JMsZCQiOP111+X66+/XtsSad++vVpA86c//UnN1kFhELKhMPW3eUXkUml/XWfxdvpTBMRrlBSWl0mxa5K0/8sT0jPtMmnSpIn3dYV0XVYjj7r+Im8+crO3Lxk/GH3YDY98U3lKtDkJGnL0lFT5CAcaYWRMYv1tM6DXathxMaZYSIhwYEoRpOFu3rxZli1bJm+//bb6Xk9rw3Eo/KpVq2TTpk1qY2Q+EbkgXxz7p3R9/JfSNZ4tc6S06CJ9h46TRX91qws71b3+ukjyhv4vyXBcqn0wfvhGH+vXr1ejD4T6xIZ0ulJa+rQiWKRt8uTJpklhnTVrltrJZYFfZIQhHN9LRdHjWk822OtBWV3+rfb5WnDjQMFxQRD+BbuRMLSFzxlbRC5Ixd7/kKJ39kqF2rs6I+VF/y7jX+spSx7vKaHrsq0LrhWuG1ZdxBogiCSJ1WgmP0nPlGypkpOnfZ7x7/9HPv3gqDi6XyftfVqR/fv3m8bfQPvy9ddfq1PtkMgIQziaiWPoS6LUHBJntsPbwyiQ0u98erY1J6R4Wks5VRX7QL+hReT0h7Ls/p6S9gMI5TBxVvaXle/+RjJaJCRoMxWIHlGoibFtTDPB6MNaBDLCPZ9+LO8fzZBHB9xSZ5iDrVu3yk033aRtGRcUJ7PALwa8jX+YaIVlnQoUr3AkFaSAoo4A5f/IsUY6LwrUiPFAmjVuK/wkZkJPxx2mOMvOaft0tCluHHmK89BpRak6pLjyG9ZxmCUNl7UasWMK4fCFImJ88EDi+uDFh9ME1M1EcPHVsP7ntFLmmqbWL9VWjruUMr8aJjyXeB6NDNoKikbsxCAcNd6Oxxol19vriHQ6i3jhLyKYHgO9CU4VYAwYfdgLFIgauRMHsUA7gTaCxEYEkxzqE+sd1bY1cl3iLhyawrTUWlBTUFpaqmb5IB3QKyLqwlE9evTgGGYK0ZerhQmJbBv4VsR6IK21efPmES8LnSy4GFN8idzZ9THHa064JC+Vqag++Brr3khEevbsKWvWrFFv5gULFqizdeLmJskF1wUzpGKJ2pEjR6qmJK+D9SgrKxNv5G9I0cD9NmfOnLoMTxI7MaUENb16qDidqY82/KGIGA9cD2TKYWr84cOHq1PrE+uAqTqwPILRwHOuL8bEFfzih+VzSSkixkGPPiZMmMDow2IgDRdp80bD6XSqP1ngF1/CFw7PN1L5xVmRs6fk9NlETqmXOCgixoDRh7WAf4C1xTEjhJFA7Zdeq1GfM1Je8qYsGXVzbQHzqKLgU6qQwMAcD813its1vi5NT3/FY7puo+CbnYXvxuys5IHzjkwXrPsR9/Nd41ZK19ROgV9732Yr+Wt2K+5UzIRvYYyYhqvXauDZrodWg6LeC853Qy5GRYITQTquPdBFBOJBEUkOOLc4zygei186p74uu7eBcB1SqvT0cYdDyXYe8m6ReIE0XCOluOqi0aBWo+aY4spLV0QvZCRRQ+EIARo03IQUkeSgF2fhPMd+jquU0oIsbyMxTSk+rctEbS1SLKsikvrgOuHZMMozAbHA39NwMSa9I5Gu5LmOseMQI5xoKQRILUT63vTp09X8dNSFbN++nZ5Igujevbt6fgHOdWxzk10q7X/6b+KoeFf+uPV47UJXqk/3kwbzK5HoMVIabsjFmDyfyuaVRVLh6CE3lP8fuUadnPVmGfX8B9rEpSQiNAEhEYDeFSORxBKf6OO0csiZp3RSl/g9p7iLZyvZKVvu15rA2zDCzAC4RzDUGexvqV3qFlOlvFrra9S4ld3P5XojEA5dRgMjjihgJJJ44hN9tJIug/JkYrsN8usuP5SMwuvk98sflW6c0ThuGCENF88aajUwnTsijkB4qk7JUUmTzAGDateoaeqQzHET5XdZIlve/JscYdQREXyCYoQikjhwbnFeX375ZXnsscfU8xnJufRUvC8zRyyRmhF/kOK9O2WyLJEbWw6S6SWJXaPdLhglDTfqxZhaOOSnHZs3WMWQNA6FI46EEhGskodlVrlOd+To0QcaKJzT8Jar/VK2vTBNnr10sNx3W2tvB/MOeWr5OnHmuuXZRZvZw4wD//jHP1JejR3uYkzNbughOY699dYU0XHk9JAbDDJ1klmgcCQIfxEZMmSIOglj27Zt1cWOKCKRgfOpL1e7YsUKVYhDnj/Pl3LsI7e2odGimwwacgd7mHECw1S33XabtpV8sOIk/oawFmNq1VsmvThRZPEiWahGnBekomS1LHu/j8z7VU8mS0SK5nWQJAETz9dYR9Eh6kYaFCqRoOAcomAQ5jnOXWD0hYnSlVznAaXKu6fGvUWZltVJySrYrW6T6ME1wP2Ln6kAz1DAWo2Q+K4p4n1l5StrSt00xqOAwpFCKCKxgVx9ZNKgAC3gOWPleMJA1hvu11SgZ9xxMabUEcF6HCSRwPTdt2+fOpY/Y8YMNTceU5FjPi3MsUUCg/OGNVgw1j1v3jx1HiySeHC+09LSgmYxJQquq2EMKBwGhCISOZgoEb4HCr+mTp3K85Rg7r//flU8kplRBU9r4MCBFA0DQHPcgPgb66NHj6ax3ggQjA0bNsjtt9+unicYpyQxpCINF52pKVOmqAkSFI3Uw4jDROiRyP79+9W1LLA4DSORhqBhw4pvADn+qa4zsBrouCDCS9YaF7jv9cWYuK6GMaBwmBhUU+/cuZMiEgREHTk5OeJyuZI+Fm9lMCSI9PJk9fz1dTWwjg4xBhQOi0ARCQyjj/iDxY8whNpo7UQc0EUjrFoNkjQoHBaEItIQRh/xAffW8uXLk9L7x3Q9qAjHapGMoo0FhcPiUEQugugDPVdMUTF58uSGU2+TRsF91KJFi4SLry4aEHxGicaDwmEjKCK1wNydOXOmarTiHHAIJHyQhrt48eKEii4EvkOHDupaHxR3Y0LhsCn+InLnnXdK3759bdO7QzrzwoUL1eygRDeEVkGvo9izZ4+2J/5ANFjgZ3woHKSeiOjVwHYREUYf4YNzhXoi1BclAqTdDh8+XK3VoA9lbCgcpB52FBFGH+GB9VAwrX0iIgHWapgLCgcJit1EhNFHaJCG+9VXXyXEE4MoVVZWqsJNjA+Fg4SFXUQE0cdLL72kjuMz+rgIrn+i0nBZq2E+KBwkYuwgIviOWK4WWURIC7V7g4ZrDeK94h/SbfG7161bR9EwERQOEhNWFhGMuyO7B5MnYt1zLGFrVxKRhstaDfNC4SBxAyLyySefqA0BsIqI2D36SEQaLhIRunbtKsePH6domBBOq07iBnrkGMpADx3j1gBGMxpcRCTI0Tcj+F5YGwUgqwhCYieQgotrGC9wH4wcOVKNVCka5oQRB0k4aChKSkosEYnYMfqIZxquHr2wwM/cUDjsQHW5lGzZLpuXLZUvnvwPKRzaQTug0djxOGIFEYH3oS9Xa4cGMF5puKzVsBAQDmJlTirF+RnoHHhfnZRc12fafp3GjieO48ePK4WFhcqQIUPUF95jn1koKytT/+7Jkycr3oZV22st9u/fr4wdO1bbig38nmXLlmlbxMzQ47A87aTvolKpKXNKtranPo0dTxyIMszsiSDDCGmk6enp6vALCgitBpIdMI9ZrOjXd8yYMepPYm4oHDahacvW0l57H4jGjieaUCKCbaMa0vA48HevXbtWVqxYoa6Oh3F8q4AhRazjHgu4fizwsxYUDmI4/EWkVatWMnv2bMnMzDSsiFgx+oAAut3umGo3UKuB6HHRokUUDQtB4SCGxldE0Ps1sohYLfqINQ3Xt8CPK/hZCwoHMQ1mERE9+sAQD6IPPYPMbEA4kIYbDfCnIBqouMd1I9aCwkFMidFFBNEHUo3xt23cuFHGjRtneLPfnxkzZsiNN96obYUPvie+O1KV7TxNi5WhcBDTY2QRwd+GGWUHDRqkLodqlugD52zs2LERDzGhVgNJDVOnTmWBn4WhcNgET1WlfCFn5YvKb8Sj7fOlseNmwagigh445mUyS/QRTRquXuDXv39/9fsSC6PVcxDLUqWUFmRpBX7aq1OBUvqddrjR49YAhYUul0stQuvVq5daiIbitlSAvwPnGT+NCs4TChwjYf78+WoxJLE+nHKE2A5kOsH4xbQhqC9AhNK7d++kjscj4pgzZ476ftasWYYykPX5pCKZDRfRHGs17MMPvGH8bO09IbYADVunTp3kvvvuk5ycHDl//rysWbNG5s2bp76/9NJLpX37xJZDYggN///ll18u48ePl8suu0zNxrrkkku0T6SOffv2qeco3KEqDAn+6U9/EqfTSdGwCYw4CNFIVSSC/3fhwoXqGhVGWK42ktlwuRiTPaFwEBKAVIgIqs1nzpypZiUNGzYsZb13JBJs2rSp0YwqLsZkX5hVRUgA0GhmZ2erqbRoRBEFLF++PKHZWfj/8H8dPHhQhg8frjbMyQb/J5YAbkw04NFwMSb7woiDkAjwj0QwJQeGdXr06BHXCCFV0QfmlQKIsIKhm+dcjMm+MOIgJAL8I5GePXuqxnrz5s1VbwBj/qhniJVURR87duyQW265RdtqCL7blClTVGGhaNgXRhyExAHfSOSVV16R+fPnxy0SwbBYMparxXdo27Ytaru0PQ1B8SJX8COMOAiJA76RCJZZjWckAkN++/bt6nuIUaKq3w8dOqQKXjDg7QAuxkRYx0FInEFEoNeJYAoO8Prrr6s1I6gRadq0qVx11VUR1Wzgs6ir6NWrlxp9nDx5UhWneNZ9YDp4/E787f7A+0BBIAv8CGDEQUgCiXckksjoA/N74e/zB38jog1UuFM0CKDHQUgKiIcnEk/vA+Y7Fp6CePjCAj8SCEYchKSAQJEIIolIIhE9+sD0JRAd/Jto2bVrV4MZbVGrwcWYSCAYcRBiICAWmCsKgoCFlMKNRPSIAYWKWAujsQI+f5AtNXHixLrKeN/FmJh2S/yhcBBiUCIVEXweQ1/wIzBhIyKacPBPw8XvgakPMz5UISCxL8yqIsSgIGOqY8eOagOOojvMoAsR6devX8DsLPxEjQXEBcNdEJ2MjIxGvQ98DplU+H900cDvQRRCSCDocRBiAtD4Y8ho+vTpcvbsWVUcgnkiGK5at26dpKenq1ODYPqSUOD36NlUGJpq06YNC/xISDhURYiJaWw4KxzvQ58NF7UmXIyJhAMjDkJMTKhIBIJx7NgxWbFihdx+++31oo/du3fLI488Infffbd8+eWXqnCgyI+iQcKBEQchFsQ/Ehk7dqzcddddqkD861//UmtIYIr7gs/+8pe/1LYICQ6FgxCL4y8iWK7222+/1Y5eZPDgwfLnP/9Z2yIkOBQOQmzEgQMH5IEHHpCjR49qe+rD5oCEAz0OQmwEMqa++eYbbas+nTt31t4REhoKByE2AlOHDBgwQNu6COpBML0IIeFA4SDEZqCqHH6Gw+FQtyEav/rVr9QXIeFAj4MQm6IvR4vUXU5iSCKBwkEIISQiOFRFCLlIRZGMatJEmoR6dV4ie7/XPk9sCYWDEHIRx1ApVM5JmXOYdyNLCkqr1BTdulfVbino9oPazxLbQuEghPjRTFq2DrKeR4tMefq9pySjmbZNbAmFgxBCSERQOAghYeGpeF+mT3lHKrRtYl8oHISQIGyTyT1b1pniP0jLlme/qNGOETtD4SCEBKG+OV5zwiV59DaIFwoHISQsml49VJzOoVJbb07sDIWDEBIRns+L5PHpJXJG2yb2g8JBCPHje6mqrL/Ik46n4gP5/fSVckX/W6SVto/YD045Qgi5CCrH03LkVW0zII5pUnx4nvRtxX6nXaFwEEIIiQh2GQghhEQEhYMQQkhEUDgIIYREBIWDEEJIRFA4CCGERASFgxBCSERQOAghhESAyP8HWdtfwv3gA9QAAAAASUVORK5CYII="></p>
</div>
<div class="specification">
<p>Daniel plans to visit all the attractions, starting and finishing at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>. He wants to minimize his travel time.</p>
<p>To find a lower bound for Daniel’s travel time, vertex <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and its adjacent edges are first deleted.</p>
</div>
<div class="specification">
<p>Daniel makes a table to show the minimum travel time between each pair of attractions.</p>
<p><img 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"></p>
</div>
<div class="specification">
<p>Write down the value of</p>
</div>
<div class="specification">
<p>To find an upper bound for Daniel’s travel time, the nearest neighbour algorithm is used, starting at vertex <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>.</p>
</div>
<div class="specification">
<p>Consider the case where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>3</mn></math>.</p>
</div>
<div class="specification">
<p>Consider the case where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mn>3</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down a Hamiltonian cycle in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use Prim’s algorithm, starting at vertex <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>, to find the weight of the minimum spanning tree of the remaining graph. You should indicate clearly the order in which the algorithm selects each edge.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, for the case where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo><</mo><mn>9</mn></math>, find a lower bound for Daniel’s travel time, in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the nearest neighbour algorithm to find two possible cycles.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the best upper bound for Daniel’s travel time.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the least value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> for which the edge <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AF</mtext></math> will definitely not be used by Daniel.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence state the value of the upper bound for Daniel’s travel time for the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> found in part (e)(i).</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The tourist office in the city has received complaints about the lack of cleanliness of some routes between the attractions. Corinne, the office manager, decides to inspect all the routes between all the attractions, starting and finishing at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>H</mtext></math>. The sum of the weights of all the edges in graph <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>92</mn><mo>+</mo><mi>x</mi><mo>)</mo></math>.</p>
<p>Corinne inspects all the routes as quickly as possible and takes <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> hours.</p>
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> during Corinne’s inspection.</p>
<div class="marks">[5]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>A graphic designer, Ben, wants to create an animation in which a sequence of squares is created by a composition of successive enlargements and translations and then rotated about the origin and reduced in size.</p>
<p>Ben outlines his plan with the following storyboards.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
<p>The first four frames of the animation are shown below in greater detail.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The sides of each successive square are one half the size of the adjacent larger square. Let the sequence of squares be <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>U</mi><mn>0</mn></msub><mo>,</mo><mo> </mo><msub><mi>U</mi><mn>1</mn></msub><mo>,</mo><mo> </mo><msub><mi>U</mi><mn>2</mn></msub><mo>,</mo><mo> </mo><mo>…</mo></math></p>
<p>The first square, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>U</mi><mn>0</mn></msub></math>, has sides of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo> </mo><mtext>cm</mtext></math>.</p>
</div>
<div class="specification">
<p>Ben decides the animation will continue as long as the width of the square is greater than the width of one pixel.</p>
</div>
<div class="specification">
<p>Ben decides to generate the squares using the transformation</p>
<p style="padding-left: 60px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><msub><mi>x</mi><mi>n</mi></msub></mtd></mtr><mtr><mtd><msub><mi>y</mi><mi>n</mi></msub></mtd></mtr></mtable></mfenced><mo>=</mo><msub><mi mathvariant="bold-italic">A</mi><mi>n</mi></msub><mfenced><mtable><mtr><mtd><msub><mi>x</mi><mn>0</mn></msub></mtd></mtr><mtr><mtd><msub><mi>y</mi><mn>0</mn></msub></mtd></mtr></mtable></mfenced><mo>+</mo><msub><mi mathvariant="bold-italic">b</mi><mi>n</mi></msub></math></p>
<p>where <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="bold-italic">A</mi><mi>n</mi></msub></math> is a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>×</mo><mn>2</mn></math> matrix that represents an enlargement, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="bold-italic">b</mi><mi>n</mi></msub></math> is a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>×</mo><mn>1</mn></math> column vector that represents a translation, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msub><mi>x</mi><mn>0</mn></msub><mo>,</mo><mo> </mo><msub><mi>y</mi><mn>0</mn></msub></mrow></mfenced></math> is a point in <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="bold-italic">U</mi><mn>0</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msub><mi>x</mi><mi>n</mi></msub><mo>,</mo><mo> </mo><msub><mi>y</mi><mi>n</mi></msub></mrow></mfenced></math> is its image in <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="bold-italic">U</mi><mi>n</mi></msub></math>.</p>
</div>
<div class="specification">
<p>By considering the case where <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msub><mi>x</mi><mn>0</mn></msub><mo>,</mo><mo> </mo><msub><mi>y</mi><mn>0</mn></msub></mrow></mfenced></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>0</mn><mo>,</mo><mo> </mo><mn>0</mn></mrow></mfenced></math>,</p>
</div>
<div class="specification">
<p>Once the image of squares has been produced, Ben wants to continue the animation by rotating the image counter clockwise about the origin and having it reduce in size during the rotation.</p>
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi>θ</mi></msub></math> be the enlargement matrix used when the original sequence of squares has been rotated through <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math> degrees.</p>
<p>Ben decides the enlargement scale factor, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math>, should be a linear function of the angle, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math>, and after a rotation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>360</mn><mo>°</mo></math> the sequence of squares should be half of its original length.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for the width of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>U</mi><mi>n</mi></msub></math> in centimetres.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given the width of a pixel is approximately <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>025</mn><mo> </mo><mtext>cm</mtext></math>, find the number of squares in the final image.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="bold-italic">A</mi><mn>1</mn></msub></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="bold-italic">A</mi><mi>n</mi></msub></math>, in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>state the coordinates, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msub><mi>x</mi><mn>1</mn></msub><mo>,</mo><mo> </mo><msub><mi>y</mi><mn>1</mn></msub></mrow></mfenced></math>, of its image in <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>U</mi><mn>1</mn></msub></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>hence find <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="bold-italic">b</mi><mn>1</mn></msub></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>show that <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="bold-italic">b</mi><mi>n</mi></msub><mo>=</mo><mfenced><mtable><mtr><mtd><mn>8</mn><mfenced><mrow><mn>1</mn><mo>-</mo><msup><mn>2</mn><mrow><mo>-</mo><mi>n</mi></mrow></msup></mrow></mfenced></mtd></mtr><mtr><mtd><mn>8</mn><mfenced><mrow><mn>1</mn><mo>-</mo><msup><mn>2</mn><mrow><mo>-</mo><mi>n</mi></mrow></msup></mrow></mfenced></mtd></mtr></mtable></mfenced></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence or otherwise, find the coordinates of the top left-hand corner in <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>U</mi><mn>7</mn></msub></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math>, in the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mfenced><mi>θ</mi></mfenced><mo>=</mo><mi>m</mi><mi>θ</mi><mo>+</mo><mi>c</mi></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi>θ</mi></msub></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence find the image of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>1</mn><mo>,</mo><mo> </mo><mn>1</mn><mo>)</mo></math> after it is rotated <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>135</mn><mo>°</mo></math> and enlarged.</p>
<div class="marks">[4]</div>
<div class="question_part_label">f.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math> at which the enlargement scale factor equals zero.</p>
<div class="marks">[1]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>After the enlargement scale factor equals zero, Ben continues to rotate the image for another two revolutions.</p>
<p>Describe the animation for these two revolutions, stating the final position of the sequence of squares.</p>
<div class="marks">[3]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>This question is about a metropolitan area council planning a new town and the location of a new toxic waste dump.</strong></p>
<p><br>A metropolitan area in a country is modelled as a square. The area has four towns, located at the corners of the square. All units are in kilometres with the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-coordinate representing the distance east and the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-coordinate representing the distance north from the origin at <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>)</mo></math>.</p>
<ul>
<li>Edison is modelled as being positioned at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mo>(</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>40</mn><mo>)</mo></math>.</li>
<li>Fermitown is modelled as being positioned at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>F</mtext><mo>(</mo><mn>40</mn><mo>,</mo><mo> </mo><mn>40</mn><mo>)</mo></math>.</li>
<li>Gaussville is modelled as being positioned at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>G</mtext><mo>(</mo><mn>40</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>)</mo></math>.</li>
<li>Hamilton is modelled as being positioned at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>H</mtext><mo>(</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>)</mo></math>.</li>
</ul>
</div>
<div class="specification">
<p>The metropolitan area council decides to build a new town called Isaacopolis located at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>I</mtext><mo>(</mo><mn>30</mn><mo>,</mo><mo> </mo><mn>20</mn><mo>)</mo></math>.</p>
<p>A new Voronoi diagram is to be created to include Isaacopolis. The equation of the perpendicular bisector of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="[" close="]"><mtext>IE</mtext></mfenced></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mi>x</mi><mo>+</mo><mfrac><mn>15</mn><mn>2</mn></mfrac></math>.</p>
</div>
<div class="specification">
<p>The metropolitan area is divided into districts based on the Voronoi regions found in part (c).</p>
</div>
<div class="specification">
<p>A toxic waste dump needs to be located within the metropolitan area. The council wants to locate it as far as possible from the nearest town.</p>
</div>
<div class="specification">
<p>The toxic waste dump, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>T</mtext></math>, is connected to the towns via a system of sewers.</p>
<p>The connections are represented in the following matrix, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">M</mi></math>, where the order of rows and columns is (<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E, F, G, H, I, T</mtext></math>).</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">M</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mn>1</mn><mo> </mo><mo> </mo></mtd><mtd><mn>0</mn><mo> </mo><mo> </mo></mtd><mtd><mn>1</mn><mo> </mo><mo> </mo></mtd><mtd><mn>1</mn><mo> </mo><mo> </mo></mtd><mtd><mn>0</mn><mo> </mo><mo> </mo></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn><mo> </mo><mo> </mo></mtd><mtd><mn>1</mn><mo> </mo><mo> </mo></mtd><mtd><mn>0</mn><mo> </mo><mo> </mo></mtd><mtd><mn>0</mn><mo> </mo><mo> </mo></mtd><mtd><mn>0</mn><mo> </mo><mo> </mo></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn><mo> </mo><mo> </mo></mtd><mtd><mn>0</mn><mo> </mo><mo> </mo></mtd><mtd><mn>1</mn><mo> </mo><mo> </mo></mtd><mtd><mn>0</mn><mo> </mo><mo> </mo></mtd><mtd><mn>1</mn><mo> </mo><mo> </mo></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>1</mn><mo> </mo><mo> </mo></mtd><mtd><mn>0</mn><mo> </mo><mo> </mo></mtd><mtd><mn>0</mn><mo> </mo><mo> </mo></mtd><mtd><mn>1</mn><mo> </mo><mo> </mo></mtd><mtd><mn>0</mn><mo> </mo><mo> </mo></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>0</mn><mo> </mo><mo> </mo></mtd><mtd><mn>0</mn><mo> </mo><mo> </mo></mtd><mtd><mn>1</mn><mo> </mo><mo> </mo></mtd><mtd><mn>0</mn><mo> </mo><mo> </mo></mtd><mtd><mn>1</mn><mo> </mo><mo> </mo></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn><mo> </mo><mo> </mo></mtd><mtd><mn>1</mn><mo> </mo><mo> </mo></mtd><mtd><mn>0</mn><mo> </mo><mo> </mo></mtd><mtd><mn>1</mn><mo> </mo><mo> </mo></mtd><mtd><mn>0</mn><mo> </mo><mo> </mo></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math></p>
<p>A leak occurs from the toxic waste dump and travels through the sewers. The pollution takes one day to travel between locations that are directly connected.</p>
<p>The digit <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">M</mi></math> represents a direct connection. The values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> in the leading diagonal of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">M</mi></math> mean that once a location is polluted it will stay polluted.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The model assumes that each town is positioned at a single point. Describe possible circumstances in which this modelling assumption is reasonable.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch a Voronoi diagram showing the regions within the metropolitan area that are closest to each town.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of the perpendicular bisector of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="[" close="]"><mtext>IF</mtext></mfenced></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that the coordinates of one vertex of the new Voronoi diagram are <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>20</mn><mo>,</mo><mo> </mo><mn>37</mn><mo>.</mo><mn>5</mn><mo>)</mo></math>, find the coordinates of the other two vertices within the metropolitan area.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch this new Voronoi diagram showing the regions within the metropolitan area which are closest to each town.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A car departs from a point due north of Hamilton. It travels due east at constant speed to a destination point due North of Gaussville. It passes through the Edison, Isaacopolis and Fermitown districts. The car spends <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn><mo>%</mo></math> of the travel time in the Isaacopolis district.</p>
<p>Find the distance between Gaussville and the car’s destination point.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the location of the toxic waste dump, given that this location is not on the edge of the metropolitan area.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Make one possible criticism of the council’s choice of location.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find which town is last to be polluted. Justify your answer.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of days it takes for the pollution to reach the last town.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A sewer inspector needs to plan the shortest possible route through each of the connections between different locations. Determine an appropriate start point and an appropriate end point of the inspection route.</p>
<p><strong>Note</strong> that the fact that each location is connected to itself does not correspond to a sewer that needs to be inspected.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.iii.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>This question compares possible designs for a new computer network between multiple school buildings, and whether they meet specific requirements.</strong></p>
<p><br>A school’s administration team decides to install new fibre-optic internet cables underground. The school has eight buildings that need to be connected by these cables. A map of the school is shown below, with the internet access point of each building labelled <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A–H</mtext></math>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
<p>Jonas is planning where to install the underground cables. He begins by determining the distances, in metres, between the underground access points in each of the buildings.</p>
<p>He finds <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AD</mtext><mo>=</mo><mn>89</mn><mo>.</mo><mn>2</mn><mo> </mo><mtext>m</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>DF</mtext><mo>=</mo><mn>104</mn><mo>.</mo><mn>9</mn><mo> </mo><mtext>m</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mtext>D</mtext><mo>^</mo></mover><mtext>F</mtext><mo>=</mo><mn>83</mn><mo>°</mo></math>.</p>
</div>
<div class="specification">
<p>The cost for installing the cable directly between <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>F</mtext></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>21</mn><mo> </mo><mn>310</mn></math>.</p>
</div>
<div class="specification">
<p>Jonas estimates that it will cost <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>110</mn></math> per metre to install the cables between all the other buildings.</p>
</div>
<div class="specification">
<p>Jonas creates the following graph, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math>, using the cost of installing the cables between two buildings as the weight of each edge.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>The computer network could be designed such that each building is directly connected to at least one other building and hence all buildings are indirectly connected.</p>
</div>
<div class="specification">
<p>The computer network fails if any part of it becomes unreachable from any other part. To help protect the network from failing, every building could be connected to at least two other buildings. In this way if one connection breaks, the building is still part of the computer network. Jonas can achieve this by finding a Hamiltonian cycle within the graph.</p>
</div>
<div class="specification">
<p>After more research, Jonas decides to install the cables as shown in the diagram below.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>Each individual cable is installed such that each end of the cable is connected to a building’s access point. The connection between each end of a cable and an access point has a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>4</mn><mo>%</mo></math> probability of failing after a power surge.</p>
<p>For the network to be successful, each building in the network must be able to communicate with every other building in the network. In other words, there must be a path that connects any two buildings in the network. Jonas would like the network to have less than a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>%</mo></math> probability of failing to operate after a power surge.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AF</mtext></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the cost per metre of installing this cable.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State why the cost for installing the cable between <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>F</mtext></math> would be higher than between the other buildings.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>By using Kruskal’s algorithm, find the minimum spanning tree for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math>, showing clearly the order in which edges are added.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence find the minimum installation cost for the cables that would allow all the buildings to be part of the computer network.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State why a path that forms a Hamiltonian cycle does not always form an Eulerian circuit.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Starting at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math>, use the nearest neighbour algorithm to find the upper bound for the installation cost of a computer network in the form of a Hamiltonian cycle.</p>
<p><strong>Note:</strong> Although the graph is not complete, in this instance it is not necessary to form a table of least distances.</p>
<div class="marks">[5]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>By deleting <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math>, use the deleted vertex algorithm to find the lower bound for the installation cost of the cycle.</p>
<div class="marks">[6]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that Jonas’s network satisfies the requirement of there being less than a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>%</mo></math> probability of the network failing after a power surge.</p>
<div class="marks">[5]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>The weights of the edges in the complete graph <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="G">
<mi>G</mi>
</math></span> are given in the following table.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-10_om_09.18.27.png" alt="M17/5/MATHL/HP3/ENG/TZ0/DM/02"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Starting at A , use the nearest neighbour algorithm to find an upper bound for the travelling salesman problem for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="G">
<mi>G</mi>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>By first deleting vertex A , use the deleted vertex algorithm together with Kruskal’s algorithm to find a lower bound for the travelling salesman problem for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="G">
<mi>G</mi>
</math></span>.</p>
<div class="marks">[7]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the graph <em>G</em> represented in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The graph <em>G</em> is a plan of a holiday resort where each vertex represents a villa and the edges represent the roads between villas. The weights of the edges are the times, in minutes, Mr José, the security guard, takes to walk along each of the roads. Mr José is based at villa A.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State, with a reason, whether or not <em>G</em> has an Eulerian circuit.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use Kruskal’s algorithm to find a minimum spanning tree for <em>G</em>, stating its total weight. Indicate clearly the order in which the edges are added.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use a suitable algorithm to show that the minimum time in which Mr José can get from A to E is 13 minutes.</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the minimum time it takes Mr José to patrol the resort if he has to walk along every road at least once, starting and ending at A. State clearly which roads need to be repeated.</p>
<div class="marks">[7]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In the context of graph theory, explain briefly what is meant by a circuit;</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In the context of graph theory, explain briefly what is meant by an Eulerian circuit.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The graph <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="G">
<mi>G</mi>
</math></span> has six vertices and an Eulerian circuit. Determine whether or not its complement <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="G'">
<msup>
<mi>G</mi>
<mo>′</mo>
</msup>
</math></span> can have an Eulerian circuit.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an example of a graph <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="H">
<mi>H</mi>
</math></span>, with five vertices, such that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="H">
<mi>H</mi>
</math></span> and its complement <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="H'">
<msup>
<mi>H</mi>
<mo>′</mo>
</msup>
</math></span> both have an Eulerian trail but neither has an Eulerian circuit. Draw <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="H">
<mi>H</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="H'">
<msup>
<mi>H</mi>
<mo>′</mo>
</msup>
</math></span> as your solution.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the following weighted graph <em>G</em>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what feature of <em>G</em> ensures that <em>G</em> has an Eulerian trail.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what feature of <em>G</em> ensures that <em>G</em> does not have an Eulerian circuit.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an Eulerian trail in <em>G</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Starting and finishing at B, find a solution to the Chinese postman problem for<em> G</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the total weight of the solution.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>Mathilde delivers books to five libraries, A, B, C, D and E. She starts her deliveries at library D and travels to each of the other libraries once, before returning to library D. Mathilde wishes to keep her travelling distance to a minimum.</p>
<p>The weighted graph <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="H">
<mi>H</mi>
</math></span>, representing the distances, measured in kilometres, between the five libraries, has the following table.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-09_om_05.58.38.png" alt="N17/5/MATHL/HP3/ENG/TZ0/DM/01"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the weighted graph <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="H">
<mi>H</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Starting at library D use the nearest-neighbour algorithm, to find an upper bound for Mathilde’s minimum travelling distance. Indicate clearly the order in which the edges are selected.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>By first removing library C, use the deleted vertex algorithm, to find a lower bound for Mathilde’s minimum travelling distance.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The simple, complete graph <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\kappa _n}(n > 2)">
<mrow>
<msub>
<mi>κ<!-- κ --></mi>
<mi>n</mi>
</msub>
</mrow>
<mo stretchy="false">(</mo>
<mi>n</mi>
<mo>></mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
</math></span> has vertices <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_1},{\text{ }}{{\text{A}}_2},{\text{ }}{{\text{A}}_3},{\text{ }} \ldots ,{\text{ }}{{\text{A}}_n}">
<mrow>
<msub>
<mrow>
<mtext>A</mtext>
</mrow>
<mn>1</mn>
</msub>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>A</mtext>
</mrow>
<mn>2</mn>
</msub>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>A</mtext>
</mrow>
<mn>3</mn>
</msub>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo>…<!-- … --></mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>A</mtext>
</mrow>
<mi>n</mi>
</msub>
</mrow>
</math></span>. The weight of the edge from <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_i}">
<mrow>
<msub>
<mrow>
<mtext>A</mtext>
</mrow>
<mi>i</mi>
</msub>
</mrow>
</math></span> to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_j}">
<mrow>
<msub>
<mrow>
<mtext>A</mtext>
</mrow>
<mi>j</mi>
</msub>
</mrow>
</math></span> is given by the number <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="i + j">
<mi>i</mi>
<mo>+</mo>
<mi>j</mi>
</math></span>.</p>
</div>
<div class="specification">
<p>Consider the general graph <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\kappa _n}">
<mrow>
<msub>
<mi>κ<!-- κ --></mi>
<mi>n</mi>
</msub>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) Draw the graph <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\kappa _4}">
<mrow>
<msub>
<mi>κ</mi>
<mn>4</mn>
</msub>
</mrow>
</math></span> including the weights of all the edges.</p>
<p>(ii) Use the nearest-neighbour algorithm, starting at vertex <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_1}">
<mrow>
<msub>
<mrow>
<mtext>A</mtext>
</mrow>
<mn>1</mn>
</msub>
</mrow>
</math></span>, to find a Hamiltonian cycle.</p>
<p>(iii) Hence, find an upper bound to the travelling salesman problem for this weighted graph.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Consider the graph <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\kappa _5}">
<mrow>
<msub>
<mi>κ</mi>
<mn>5</mn>
</msub>
</mrow>
</math></span>. Use the deleted vertex algorithm, with <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_5}">
<mrow>
<msub>
<mrow>
<mtext>A</mtext>
</mrow>
<mn>5</mn>
</msub>
</mrow>
</math></span> as the deleted vertex, to find a lower bound to the travelling salesman problem for this weighted graph.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) Use the nearest-neighbour algorithm, starting at vertex <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_1}">
<mrow>
<msub>
<mrow>
<mtext>A</mtext>
</mrow>
<mn>1</mn>
</msub>
</mrow>
</math></span>, to find a Hamiltonian cycle.</p>
<p>(ii) Hence find and simplify an expression in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n">
<mi>n</mi>
</math></span>, for an upper bound to the travelling salesman problem for this weighted graph.</p>
<div class="marks">[7]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>By splitting the weight of the edge <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_i}{{\text{A}}_j}">
<mrow>
<msub>
<mrow>
<mtext>A</mtext>
</mrow>
<mi>i</mi>
</msub>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>A</mtext>
</mrow>
<mi>j</mi>
</msub>
</mrow>
</math></span> into two parts or otherwise, show that all Hamiltonian cycles of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\kappa _n}">
<mrow>
<msub>
<mi>κ</mi>
<mi>n</mi>
</msub>
</mrow>
</math></span> have the same total weight, equal to the answer found in (c)(ii).</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="G">
<mi>G</mi>
</math></span> is a simple, connected graph with eight vertices.</p>
</div>
<div class="specification">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="H">
<mi>H</mi>
</math></span> is a connected, planar graph, with <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v">
<mi>v</mi>
</math></span> vertices, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="e">
<mi>e</mi>
</math></span> edges and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> faces. Every face in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="H">
<mi>H</mi>
</math></span> is bounded by exactly <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> edges.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the minimum number of edges in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="G"> <mi>G</mi> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the maximum number of edges in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="G"> <mi>G</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the maximum number of edges in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="G"> <mi>G</mi> </math></span>, given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="G"> <mi>G</mi> </math></span> contains an Eulerian circuit.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2e = kf"> <mn>2</mn> <mi>e</mi> <mo>=</mo> <mi>k</mi> <mi>f</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = 9"> <mi>v</mi> <mo>=</mo> <mn>9</mn> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 3"> <mi>k</mi> <mo>=</mo> <mn>3</mn> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the possible values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = 13"> <mi>v</mi> <mo>=</mo> <mn>13</mn> </math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>A driver needs to make deliveries to five shops <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A">
<mi>A</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="B">
<mi>B</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C">
<mi>C</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="D">
<mi>D</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="E">
<mi>E</mi>
</math></span>. The driver starts and finishes his journey at the warehouse <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="W">
<mi>W</mi>
</math></span>. The driver wants to find the shortest route to visit all the shops and return to the warehouse. The distances, in kilometres, between the locations are given in the following table.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASkAAACtCAYAAADsz4n4AAAgAElEQVR4Ae1dv4vkRtPWvzHxpps5u2iiSS5x4sSBgk0uuMDgYGCDAwcGB4KBA8OBYWA5MBgOwYF5wRwMBx8HZmF4ecG8LAMfH8YskzgwywbmOIb66FaX1D/1o7s1UuMynEdqtUpPPV1d6m71VmVA/xEDxAAxMGMGshljI2jEADFADIDipLIsA/pHHJANkA1MaQO6XzaclF5hjueMwLn/RxjjtBDxSDwqvT0Fg2BNlgJOwkidKw4DcaSkbI/kpOLYgCElZaMwlJmwgHiMQ37KPJKTimMDhpSUjcJQZsIC4jEO+SnzSE4qjg0YUlI2CkOZCQuIxzjkp8wjOak4NmBISdkoDGUmLCAe45CfMo/kpHQbeLyFl9t/wye9fOB5uFH8DYftF44tIQtYrl/D/vhxICq1ejhGVd7puIe3bwrIF/gJfwXr7Rso37yC7fs/1co9z8Ix/gFlfmHlcZEX8ObtHo6nnmAc1cIxApwOW1h1bQFabeHgiTUE46d9ARcKtiUU+/+avOYlHAFArn9R7Hv3JRdGclKy4Z1+h/LqEoYQK98uH7sIl+v0Oa4bHA308TfY5pdVpxNG0UeOrU4sjHA6wv5mDUtmyMs13OyPwPvS6Qi3mxwW2RewPfxtg9BZFgfjR7gvn8OC4bsoYP/pBI+HX6AQPC7yG7h79Oz9Mb82P+xgzR38Albbu4pDxtDjAd4VOVwO6PA6sWE8nuBhd13xJ7fl4y0UywVk2QKWxS081g9lL9ivYV3eSWX1ReeBCyM5qZqyv2BfPOWdfz5O6k/YrT/jRtAYLZZlsFjv4KHGP/zAZRSDJJ3uYXe9qpzmcgN7vbOf7mD7+Qb2nkPTKBihGZXKnJ3uS7iyOYVBBMTbEtOMpixO/eFXKD1Ho0ydUB7rlyV38oIg1rYr5qQuIC//wEJ4vPsJipvfBjmoNozkpDi17E17DatlNS2YjZOqjUAYrTRiWeTfw+3k0z1phCK/YYW5Vj+PsC93fBqgFPc8Ce1c1WNwyvcZrHfytBPLM8gCRqVxMEqjFRw1A8Dp/ld4/79+o1CZ4jCMn+BYPqteRDU2ue0bXk/3b+H6xTuvKbQLIzkp+AjHXQHX5W9wWyxnNZJq3qy4xsN+LW9Z2RoHHLuMoreIenoSPqpzPTMYIxNc43wG5VEe0klOSh4huMA4yqNgBBwh41RPTEmvvoXdg/9UFCGHYZScFHfmrM+8gs32O/iSr1WxNapHADb9y1+ao2kE0fHrwvgPd1IneLx7DesNm08/wn5WTqoxjGqKwoy2hDVfA1jB9e6+WbPoaHzXZZdRuOqr5dKbP2vepGqd8LMwjOz5Es56FCBw1SPVDDL92gDo4RhlRyq/kMJGeLIKYRibvrFYv4N77DPHEnLupL6A7d0dlM/WUN77f8xxYfxHO6nTcQebzU4MTfFNJs+v5WYeduwivL8UxINvVnan1OEW18Fv2DCMjRPNMn2E0l/LrpphGJl0G4/iqfUIS+a4C5F5PRyj1K61s2SjlW/hSl5ANx/duyQMo+Skvswhf1bC/Un+IrmEPL8KfnG6MP5znZT8lYy/DfANNhMnVXcgeXonGXMEx+Ayin6Wn4iTsvLINGwW07PF81FGAP14ZLXQkWrT5k//hd3/yGto/SXqNcPaWpoWS1zVi+nZJeTb4QvlfTH+M50U+yK1eQU7ZeEZG2IeTqpej6rfrGwgVW2RYAYXMj1B4wgzXPlNKjtSlA5wOv4b3h9Cvj+GfpWSnLoy8mTT/Buxn+spFPu/GtAeR6E8NmtmtmnzRzje3njvM0N1wjBi35C5arhdXFUjK3yW768L4z/MSbF1nffwZnsDb/XOI+35aD73+9Id2Lmkz/r1J3OxV4bv9clkY5kII3/sA9xtr/j+mUW+gXc1pw9w2P0I2/K/gz9D69q4DFevZz2XR8v49Y59IS3FhtNFDptbsafLKqBfYRBGkL+SydNmxmEJ2/UKMsXB9sOk1wrC+GkPxYU+WhIjadu2E/3hPc9dGP9BTqqZVzMy5G0GzbA13pTPRXhne9WLkYhF/mU7zX+At7hZslNYewVvjIpY1pl+qjdGMplsJ3c5KUZ5KirzVx3zneblezjoe7oUvfqfePPIO7+Jj8lr/oWtl6EW3hiZgE972DzXR0t/w+HmO9jehY2UER/7dWH8BzkpmY7xj12Ej//k/k8gjP25aqtJPLax0/+ai0dyUv05HFTTRfggISNXJoxxCCYex+WRnFQcfg0pZLgGJV4FxKMXbcZNKfNITspozjgFKRtFHAbiSCEeiUdyUnFswJBCncugxKuAePSizbgpZR4NJ8WUoX/EAdkA2cBUNqB7WMNJ6RXmeM7Im/t/hDFOCxGPxKPS21MwCNZkKeAkjNS54jAQR0rK9khOKo4NGFJSNgpDmQkLiMc45KfMIzmpODZgSEnZKAxlJiwgHuOQnzKP5KTi2IAhJWWjMJSZsIB4jEN+yjySk4pjA4aUlI3CUGbCAuIxDvkp83heJzWbdFFxGr5NirdRPB5gV/4A6+WlFNxefpL01/H4l/3y5QHHXhjrDDDiE72cHUY8+3S8hRv21/u4ncVSpy9ML4xMeCePLH44JmLA7Qb2kDNdWP0wshAs36vpv25ujdjgp+MH2GB2oCl4rJVnQfi+gWUmQgXX5Swkz7gYz+ekZpguSuI5+qGf4TbBz9QMHAivieHDHcDZnRTLqPO8TlXUGKcUOgZjXi2voeShWzCcyzkdQBePjE+my+daKibkedjv8LY+weP+JeTrsorEUDt+LTUUDx90ActrlthAOAkp6NwQlMMxqtIbh645qTNgPJOTmmO6KLURYp+FGEUV8K4l+B7G5j63k3p4DwWPB9+whcH56tA3IvxIHQeLVeXhZ2wB3Ro5rqOxeOSd7iIsIidiHo7xT9gVP6gJC7BN64QQInKoHEtK1FG4RRAdv8MxSgL5i+cJLJcsvZrspM6D8QxOaqbpoqQ2GOMwyCh4p25xUiAiJZ7bSdmI0h0QjqSkNz53ZHJns8lxlI3DozTSWuRQvAmLLRWEsda7atPaAaHTUtrY4hTq+9sP/DGykfAzWBUf4MDTWklO6kwYR3ZSbIg6z3RR7U0aftXfKHDkkYKTEtNP3QHxiJjLKu41jzL6hXcM7FF5ZFE637L1vwVkiyvvAG5BGNHUeCx2abQpYrPXI1ReD4P5DZ86+2Fk09INrHiG548i957kpM6EcUQnNed0UWgZ4/36GYXAk8pIio+alnBV/q6l12KLwq/g69UTWAQG6R+XR8E3hhn2DIUbhJFDqEIIX8ixwrkNqBFkAdBJSY6ipwl7YeR59L4VuQAszz4TxtGc1LzTRfVs2YBqXkaBz0vCSbGO9RWsCpazUP5PLPDyDv938wVr+Y2W+EK+x308Lo/Nc6u1teGdn0kIwsizFJdwtdJS1Lc6gDOMpPgI+LmUpGKok4qHcRwnhW8m/ARd/7ZNYRqD6ToKNYpKPmbAwM/P8RIxBhvu7J2UGCXb0mnzKYAclxszs8hlXS3cXA9q604em+dUGVsmcFKsr6wL04FbF8lFnH59ei2p4ToczKNwkuw+6z+2VnYmjPGdVALpolwNGbN8sFHID+/sXNMunJ+O7+DF+jXcWRIZVCMS3SFVeNX1FVlh9/G4PDbP5bjPPd1jfeXFC8damGWR3OoUGh3ajoJ45IItIynMXSg7zREwRnRSiaSLamvJiNdCjMLe0SVwwhBCc+/5YLQ6KN7ZXlYZlRFbvRCNmwClvVSSKl2HPhhRpovH03EPb8t/wZ7nXcT09Z9LUxuU0O/XC6PVQTGuNlDsqoSg1d4kTCX1AIfyGpbSV9N+6KpaXhiVB9icFG6IHRdjJCeVSLoohfRxT/yMQuWRycjqfTMVXjP9lt8UhUkbipE5qGv2JcwyBag/nbM1lsl3nLfzqOrB0oRtYVfnDBxuF0N5BOagrqUd+TKf8qgE0IEKzusNsmfAaDzC7qTgDBgjOSlDo1ELBhvFqGjswgmjnZehpcTjUMbs9VPmkZyUvU2DS1M2imDlIwogHuOQmTKP5KTi2IAhJWWjMJSZsIB4jEN+yjySk4pjA4aUlI3CUGbCAuIxDvkp80hOKo4NGFJSNgpDmQkLiMc45KfMIzmpODZgSEnZKAxlJiwgHuOQnzKPhpNiytA/4oBsgGxgKhvQ3bLhpPQKczxn5M39P8IYp4WIR+JR6e0pGARrshRwEkbqXHEYiCMlZXskJxXHBgwpKRuFocyEBcRjHPJT5pGcVBwbMKSkbBSGMhMWEI9xyE+ZR3JScWzAkJKyURjKTFhAPMYhP2UeyUnFsQFDSspGYSgzYQHxGIf8lHmM76QwVId1K8MK1pbcYkObwZvwrlxsXdcHAPXGOOAZoVW9MNbpl8QnekcuuCYFEn7KHx6pkek3HkY57x2LhPBahG4ZzqoXRpCfn0HGEkK8O6hRTnty3QfxaBjrh4tQTUUOC973n0F5/FRf7XPgwhjfSXE0GCoDg59hdEZmsOHROV3KtBMhZQixYui63i5dv+qHUZcy7vlwjD3y7nHIU+a064OxSjCwzFZwvbuHkwidspBjjA+gfjiP7PmvYL35UCUDrUO3yI68jx79QY6DEZ8vYl1lzNn/AG/3Ry3mPdZr/3VhHMdJiSwSWSaRXpdJGTHaMTuvupRx3iBdqAKhuR1l13VJVOthCMZWwREvDsbYJ+8exuyeKqddH4yW6JFVu/vZ5mAebW3Io7FKz++jh02Oo2wUjPxZVRKJ0IQbTJQL4yhOqmrwDDByZBME7RJyfHs4yOxT7FKmz71Vokq3k+q83ushbsJ73n6WakE8IkK9c4E0Ip1LTjsNo/VFZHFcqGLXbziPVWowJVuM7aGaHrYqrrKxMOK03ncUKuN1YRzBSYnYzPqa1GoLh5MMyf/YpUwvibyhyUkxroJ45GQ78u6xa7PJaadjFOdKJl4GWMSN97DTMB4f4PBuA/nFdRV+mfNq+5+uh62Ou2wcjNjXLyH/7hvIF9X64yL/Hm55aGY3HtsVF8YRnJRo7AyHrjhfzSDzTGukK+RSRq9nPScnVdMSxCOT4sy7Vz8CADMHnTvJAUIwMLrC4Aq71cI1o5i2X28eRUp6dj//1xa/3NCjDZF5bRSM+JGs/ngifQyI6OzjO6l67Ulaj5KmAHIsbJPKfiXehDPx5KRqkoN4BFfevVp8fVBNr/xiscfH2OGkInaumoCOA5YYohRfxez9oz/XrkeF8cgGxhaMwsmqmNmC/1NQ1qNdoLRyF8bITgqH0s16VIVDWqdQcttrKHueupTpdXtSTgo7FH7GZ7/DP+26ePHnsSXvnu1h/MV1biflxmhdJLd2OJsyZpk/j5IsHJUY/cOth3R35+EoGK2coc0Ob28XxshOCueouPWg4g4X17JMLe9k1lHBpYyjulqclJNSocc+8+XRmtaqBRx3Cmee7rVitCySWx1Xi07yJV8eZRnAZxtPYKllhG7VQxXQejYORjH4UDLcCCellLVCqy+6MEZ1Uk2qIFyPYhu8foEiv6zm3J6GWmshDlzK6PVs55Uxup1l13WbTFtZCEabvDHKfDBaOw3PIVfl3ZtDTrsujMCnqs9hgbkBH++gXK/A9wuVD49qe2JqejUVfbceqpS2s9Ew3pdwtVjA8vod3/NV+YDPIN/+pm5MbQMnrrkwRnJSOMSTpyXy8QrW25+9d/Tq+rmU0eup57jBVMKlLJJ2XVeldZ35YeySGvf6UIyVAbbn3VPrnD+nnfp8qa2zDNS1E+mDDt+EWMLBkpG5D+NDeQTAdRvEZ/aP/nr0QejzJbcbY/VkLTdg5v9XJS4eIzmpfkTFquVSJpb8GHIIYwwWfTpXnOcOkUJtPYQtd10Xj+Sk3JwFXXERHiQ08s2EMQ6hxOO4PJKTisOvIYUM16DEq4B49KLNuCllHslJGc0ZpyBlo4jDQBwpxCPxSE4qjg0YUqhzGZR4FRCPXrQZN6XMo+GkmDL0jzggGyAbmMoGdA9rOCm9whzPGXlz/48wxmkh4pF4VHp7CgbBmiwFnISROlccBuJISdkeyUnFsQFDSspGYSgzYQHxGIf8lHkkJxXHBgwpKRuFocyEBcRjHPJT5pGcVBwbMKSkbBSGMhMWEI9xyE+ZR3JScWzAkJKyURjKTFhAPMYhP2UeyUnFsQFDSspGYSgzYQHxGIf8lHkc10nxONc/NqFaRMqbsvwRNtsP8ODJvw/hp+MH2GDIGI5Dz7P2EY7717Be4l/5nz8XWzfGirAmPhfu5ZGjoPYn1YfH/tLj1PTG2DuH4gMcdj81NmoEnevWww+jFGqX7020RA9IIu+eiNEu4ptndSjhbt70Gi4eR3JScoeXyceGccdz0oHbzl3K2OryssdbKPIXUB6YW0QMLOb6BvYiPEfV8ZljEiE7MDa3RzhZ9swxMFb6sRAanxvB0Zy6t1wYjLFF1liX/DBKkWCtORYFWhFHKmPhRQJCCQ3HyPLuvYQcba12RgupXVk7P4d1ecfjMjUvsKdQ7P8aTLcfxq7cgCKdFcblgge4217BIouLcQQnJQJ48beDDSyL3vkVFPvHwUTjDcMIZyGNv4eN0rAYQbQJcfppX8BFnTyCPck/wiC7ewyMTC53plPltMMGOOPvMB5VYFUAQ0dmIJ7Y4BKyuoOp9w45G47xT9gVP9QvSP4sDB+MMc5SyLsnMF8Ue6hzFaMeHi93F4/RnVQzFXGPlj7tf4afB6Zglo3GpYxcp/3YdECIu4nOWDkyNVBau1T56hgYqxCzn1V/tjSXnHay0iMcB/HoDBXdJLS8Kn/3yrYrqxqEsRZUZatptTeuD0a9rW/sdRCOscpfoOQG5HgyUJwUiAHAXMMHq52oK49YL26tlcIJr6YDqkGIVPAXV7C9ewAeGXH1jB9bQXQUjoNRPHQ2Oe06SIhwOYhHl5PCt/0ih+++y2HBR/2X3olrgzAiRzxZRZsDmmHePZEZSu1HOEsZnjDExWPckVSdzkoP1YotEefXpUxf6c4pE18b+ApWy4vgacBoGGUlcd1MWluTL3cdh2Lskh/jehBGh5PCOPbLtfh4Iq0JrbZ3g0dWQRg5SdXIThml6OTNMe9enapuZa6dzXYkJYZ/WdtipU6+x3mQUfDG/tJcfGTJBK6fVguXktFigPmhMEfBaAFRdbhmbc1SxVkUhNEpNe6FIIwOJ2WuPwIA+7jCvuxGXEvpywR/aa6ajzjmfTPNu8eA1h8f2JfmFayLr2FpxJM3NbKVuNo67khq9k6KfX14AS9299rbEvMFyp/y8UuFXGaj1l7mItxeWy51YZTrSMeT5LSTno8fGJQQP8OH+rJE+difR3ciWKuTwjTruHAtg+g4DsLIRsPrAnbOtOQzzrtn8IL9yPbBzKhsFLh4jOukcK7vyq/H1lLeHwanutG1cSmj11PP2VfHAtbWVDs4j9YcEne65xyltGFUtcEzPpKi6R7Sof46RlJgXUvpsXCtSq/P/OyRf6qF3YsXreuebG30xfo13HlmskGQ3hhRAP9la7lmbsCqiljTZemttNyBioiWExfGuE4KEGgGGfv69A4dEkt7s4Ob7c/BZDMdXcq49bd3fm4AxXu+qbSaNmWwyG8qjHz6t1L2Urnlm1dGwXjcw9vyXyI1GKYS+tycuppwrCXDMVrFjFoYghHXnsx1Jvy6t4JrPqoW22Y8tyN4YeS5CnUHxXBsoNj9yTm1Oigpx+EQ4r0wKg8QHC3V3IC8Cts4u13DMvP/+MDkuDBGdlLsUazzvIc3Irc9ezB3WOWeJw9U9PY8cSljFyfIVaYjuFNb/poib0Bl18+547wfRv7FUdkRv4Ud36Bq17yrdBiPXdLGue6HsU8ORTnvHtvYu4ab/VFbBuin02CM+AK02aRYcFbbGu21+lW/po2EsUduQBBp1qu+8gO89eQPNXDxOIKTwkeO9+tSZrwnDpdMGIdzZruDeLSxMrwsZR7JSQ1v7153pGwUvRQ8UyXiMQ7RKfNITiqODRhSUjYKQ5kJC4jHOOSnzCM5qTg2YEhJ2SgMZSYsIB7jkJ8yj+Sk4tiAISVlozCUmbCAeIxDfso8Gk6KKUP/iAOyAbKBqWxAd8uGk9IrzPGckTf3/whjnBYiHolHpbenYBCsyVLASRipc8VhII6UlO2RnFQcGzCkpGwUhjITFhCPcchPmUdyUnFswJCSslEYykxYQDzGIT9lHslJxbEBQ0rKRmEoM2EB8RiH/JR5JCcVxwYMKSkbhaHMhAXEYxzyU+YxspMSscNt2xh4TG78C/4w4v0Ir/7wueR/re2Kd4R/HS99fvYIgsa088HYZARhz3f9gbOU7cZZpx+/Phi55Nmni+qnf6xa3jwCS6dVwna9gsyWSqsOvijs8Zx/BG2Qg38Er4UuOgPGyE6q0gyTGmSZUOjxAO8wKoJnOAyZMy+jkEIbZ5nDSfHojP6hT4Iw9ki7xSNM7DewzESIEfHX9E3yCBlB97EXj3XIWNZxHJlY2KPriI3nThfVrXfsGn48YoA44YAMJzV1SiuVJaNP88vnwTiOkzpsYcVGU3KcY0whxMo9RydIm59RsLsxuJ3NSfWIM40AevwOw8gMtjvtFoiggnKojipmkhxypgc4UWUYRlVu9VyHk8K2nuqFpEId/SyER2xTYyQ1p5RWvD2fwHLJMhVJI6kzYRzBSTVTPrkz1Xns+FTQ5iT625K/USA2y/OlkdYiL+DNDgP29ccl1/THiFIsabe489ccg8VxoYSu3yCMrqiXgFPmS5hPuqguJsKuB/GIYYuNkZQFE+f83C8kFs76GayKD3Aon6lOygIRRsA4gpPC7LFaZ1JiYUve2KZoR5m/UbQ4KfHME4t+ydetpCidHXhsl/0xojQ97RZOD3TuqrC3PqPTIIwuJ4UhpOeULgopHek3iMfeTkq0vzw7GaCPH0aWaXkDKx6t9iMcO53UOBjjO6l6RKLFC6+nWmwOrl8bwLbnonT1hG4nVdXDMMjx4zX31dRMu4XYHU7q3AkEHE4KQ/bOJ11UX8b96/k5AHyeeMl0jaT4lGvpPTr1wsjXSb8VSSJc9od6sKC8v0N5FR9jZCeFb3vbuhOOsGzXJEV7HHoRzuUi0ZbpnvFcsX7l0fmZKH+M2Nh62i3E7nBSHut8QRgdTsqaiWXCdFFGs45QEMRjr5EUm0J/BSvPBAde9sg/yjyX4ue77A8JHQ9jZCeFjshMsV69YdkoKnytwt8okOg+Tko43LM7KXdKK+siuYgzra7/oeG0//rzmEi6KFl97lTFlzS+LqovR8iVhx0H8djppCZKaWXwJXOXgbrQPy7GuE6qnuppi3uYaZft6wl4G6Dp+BvFECfFRlJfeuP1w8j2orjSbrER1h1sVwuQHZLVcSFRHb9+GIVQx0hqNumiOnSPeTmIxw4nZc0Y4wE+DCN7IPYdfSQPMDbGiE4Kk2kyj4sjFZaBpYQiv+QjqHzzIUrGGH/CcQuCvibGcP4LyreY0UZkEvHMZ8eadDhGu4PiBiDSbgF+OcNP+2Iv0nn3SVU9BNeeZpkuyqMTh9wyvK2lp+GHBst03dr5J0tpZXdS58AYx0m1DQ35TvO3QamXpCblh15GUaffaYatF8UePnGJuJsWr7ENiDs4BCRkHIZRfz7iYL/aqJTtUi6veSrrald66Y1zGEZshZmni0KYZ/z14xGgWr+T27oZpbDOf12nL5PrZMpIuq+avhgb+aaTOhfGOE6q0eQsR+GEjw+TMMbhmHgkHslJxbEBQwp1LoMSrwLi0Ys246aUeSQnZTRnnIKUjSIOA3GkEI/EIzmpODZgSKHOZVDiVUA8etFm3JQyj+SkjOaMU5CyUcRhII4U4pF4JCcVxwYMKdS5DEq8CohHL9qMm1Lm0XBSTBn6RxyQDZANTGUDuoc1nJReYY7njLy5/0cY47QQ8Ug8Kr09BYNgTZYCTsJInSsOA3GkpGyP5KTi2IAhJWWjMJSZsIB4jEN+yjySk4pjA4aUlI3CUGbCAuIxDvkp80hOKo4NGFJSNgpDmQkLiMc45KfMIzmpODZgSEnZKAxlJiwgHuOQnzKP8Z0Uhp5o3cqgh0oZ1hA+hPfKaafkEFvB+ubWO7RMOMZLyItfjAgHvfToSacPRlA4yiCz5IKbHCPTvyM34Cww9mynGNW82lp5MEbqaCI11Jc7uK7rdRy4MMZ3UhwIRujUQwU/wOHdBvLLAvZVjJQO2PbLLmXstZnB3kKRv4Dy8AAsJtPx9nvIF6yDbWBfh2NhOcSeQrb8hsd0rsJQfHa+mNKPt7BZv4Lb48cK4+4bWGZahNNeejhZMC4M5hF65FmbHCNTU7I/W27AWWA0mmPUguFtrcKx593rwbUqpvXMhXEcJ1WPprROxiH+Ce/LX4G5C9//XMrY5bEwwN057cwIlyJA3lmzc8gaVAH6myic/fSQJXQdD+MRADrzrM0Ao6R01aZ6mOB5YZTgjno4uK1lNK68e1IdO9dShR6HLozjOKk6jLA0rTv9Ae/f/x+ceoDtquJSpuu+5roI4FU7IIzYiRFFq5qm42okdB0FY2QcXjyH8p6NrFz/6Xq46tnLgzEysTzgoR6YT37ehBhdIY5lePx4QowGlnEK/Nu6Z9693ly79XNhHMFJsTfVNSzYmhSGROVp1r+C692fboQDrriU6S+img40oxQxPdCTLnDibaPB7if5YzzB4+EXKPIVrDv50vXoxiXX8MeIUkRb184ey+XfCTH27jgTYpSpGvHYr60H5N3rzbVbSRfGEZyU6PDGwrk6SnFD7b7iUqb7zqqGmdNO5D6zOqkMmjDDfZ/guyteD83bnlnH1KM/PlYzlMc+edYmxdiz40yKcViTedf2amu+dtcz715PrtsUcGGM76QsUz2+CH11A4cYc73QzsXn13pOuzYnde6RFMsKc4R9WVSL+65RilWPNhMwr7mMwqxpK+mRZ85hPE8AAAj4SURBVG1qjH06ztQYbdSOUDa4rYfm3evDdYdeLoyRnZQ01VM61yP8e7cPWiyX9XMpI9exH7ty2tkXya2JLu2CjVJ/jCjKvk5WXXXpgff2+/XH2CfP2tQYcb1MXziXuZkBRhkO7+hy9IU27PKN3ceD29rAIuPS8+714dofY2Qn1Uz1mvWeBhzbm/Jy+yHYWQ0mnEOwp4xCdOYiud1xYf2uXz+MslTh8JVtEux6ux6yhK5jX4xsZPxi/Rru6u0b+pOmx8gRtb7dZ4JRp26kc9+2buCIjwuZZZ8Uq9TKdSOl7ciFMaqT4nN7tv9I2ZvCFoLfQ7ldw9JIz9QG2X3NpYz7DrtB8s6GOe34sP8SFvkN3D1+gsdDCevlGfdJaeCrfVpP4Xp3L30R7aGHJqftdDiPjkSQSi646TGiztWLxzZdnw9GxDr2r09bq5janZSba1VK25kLYyQnpS/4akNDXETHr31tSHtccyljv5UZJNsYacOkfToXyTaZ/Cxbwbq8g0e70M7SYRirrygNxgUs1z/A2/1Rc1A99ehEV1UYhrFyUO254AZwPRLGSqzFHuuPInPB2JOASNWGtrX5WJeTauPalNJW4sIYyUm1PTr+NZcy8Z/kL5Ew+nMn30k8ymz4H6fMIzkp/3ZvvTNlo2hV7MwXicc4hKfMIzmpODZgSEnZKAxlJiwgHuOQnzKP5KTi2IAhJWWjMJSZsIB4jEN+yjySk4pjA4aUlI3CUGbCAuIxDvkp82g4KaYM/SMOyAbIBqayAd0tG05KrzDHc0be3P8jjHFaiHgkHpXenoJBsCZLASdhpM4Vh4E4UlK2R3JScWzAkJKyURjKTFhAPMYhP2UeyUnFsQFDSspGYSgzYQHxGIf8lHkkJxXHBgwpKRuFocyEBcRjHPJT5pGcVBwbMKSkbBSGMhMWEI9xyE+ZR3JScWzAkJKyURjKTFhAPMYhP2Ue4zmpT3soLtS9JRfFr/BH+UzbdyXCCMv1679Q79cgoYRXYVAWZlhgJafcPPPuNQw9wGH3ExT5ZcVvXsKxudjryItHhaMMFvkG3vFUYdIjeUz7vIpzn7GIDq9hz1N1SXV6HnphlGXzCJMryDQbm1fePYzMYInVNHJOO5mqqY9dbR3PSTEN69DBcgwfkc+ObRLVAridDjdwtS6NBJhdZLmU6bqPXxdxo5gMNXZ5Ann3UME6pMwK1tufz+gA/oL95gVsbqsQMujs64QbDJ8Sl+sE8PgbbJkj1doeVen6DWprYCGOn1fOUnZSM8u718Rh051UE0RSjdHWxZp5PYxHU94YJS6McZ1UPTqSycYwuFrI0cff4Kb4qSW6o5sGlzLuO/BKZbQXyyU80ZzU/CJz6nn3hA7oZBdXsL0LyV4YY7+ZmQqq4lFuf4CQgGj+bQ1QJVh4AssnC2kkxSKedudhRIvp8xuCsXLqT2C5/AwyR9TLir+wUMJBGPuQEKGOC2NcJ1XHRW7y7TVviQzqkMKso10XPFOwj24uZdplsbjcN5CvNrA/vIFccVLoSNWMNqbjan+CfNUPoyTBmncPRwbtWWQkKa2HwRh5puCVlOXZERhNJIut278VlXrRGyMfwbGEG/+BMr+QnJQqvzozna2tlqvMGyOwGOvPYFV8gANfFlGde/28EUPz1s+YwYGLx5GcVNXZT8cdbDavoPjygq+bVNMrNq36Cor9X960uJRpFciG+Ktn1ehDONNmuieG1fKUgAnj9eSpa+sTlIteGLmElrx7mBl6kcN33+GazyXkmw9w9MjE44+Rpa4/wLsih4v1TopZj4k4tIiniPtc62Y8HfyXkG9/g0dwZAJSWqtqfx8nysT48TiPnHYKDROfuHiM6qSq7CoZZCxTzP1/YLt+BfvH36s3WcY6+3/gj3INz8rfpbC4w5lxKeOWxBzj8yZeuOGkHIZs1HM/Qb8yHCOToIdiVUdMOG2qF6LrRezzOtK6ncUfoy+uSrhHJ4nrkstrKPmC+kc43n7P03P5OIHhPLLO/xLy63fCcTvaVmqwalrYlS1aukE7HI6RNfUtFPn0Oe00VSY9dfE4kpP6HPJ8XaUIx7co+8qT55Lx+PPhUsYukX05+Rby4raJV244H4chTzKScufds6bYYsa+XDTZou0kWEuH8aiL+AjHfSm+LsojJzYSZEksFtVXx+XXUKxXkHkm4RiKkS/m5y9hX2eycbQtqsPX+PQ8jHix3+9QjDCjnHb9NDxPLRePEZ0UrkewbQjSCKBeTGefq1kmFnzl+ivuUsYuURipMwQNm5o+wmH7RTUCfGjwWZ2C/SFG6TCMxu0AYK6T2fF0dEKbaFEWjhEXxdsWdcVU+ixf92QbVLfDMF3NL2QT5d0TL8kKkwWnPi3m9ds4bmnkiG1dibL0Jx1vNxxrDZc9juCkFrCURy04/F/4D6d1jVzK6PWc58ZICjubPCKYYd49waU6baqMRi1zaq5cCOaRSeOYnjrWGJkTuIJF5rquwLGehGN0OXE2wi5gzdetrI/uXRiOEZ0rLZzbSI/opKr1FGO0xB2Cv5FaQYfGk7I4KXV/z3zz7lX7flZifU1sAvTcjhDcufi05Sks6/UfbC025dvBlk3zFnm9rwqvDvkNxmhdOLc7KDZVfIF5GAeADMfY7qRwLXK1vfNeyw3HOIAQz6oujHGd1Oabah1KAnk6/AjXEd5WkkjPrymSBJuTYpfrTZJsCD63vHuI/wEO5XWTR3C5hhslPx/W6/51GYXzTlz/wqnzcg3bt3vly2KzqB620RQxDMaIN9a/+khKOHbUQfmVR9K1gM6DcIwuJ6V/SMk6tlK4oYZjdMuOdcWFMaKTigW1W45Lme47z1eDMMbhmngkHslJxbEBQwp1LoMSrwLi0Ys246aUeSQnZTRnnIKUjSIOA3GkEI/EIzmpODZgSKHOZVDiVUA8etFm3JQyj+SkjOaMU5CyUcRhII4U4pF4NJwUMwr6RxyQDZANTGUDultWnJR+kc6JAWKAGJiaAXJSU7cAPZ8YIAZaGSAn1UoPXSQGiIGpGSAnNXUL0POJAWKglQFyUq300EVigBiYmoH/B9Cutq8KHFpqAAAAAElFTkSuQmCC"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>By deleting <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="W"> <mi>W</mi> </math></span>, use the deleted vertex algorithm to find a lower bound for the length of a route that visits every shop, starting and finishing at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="W"> <mi>W</mi> </math></span>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Starting from <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="W"> <mi>W</mi> </math></span>, use the nearest-neighbour algorithm to find a route which gives an upper bound for this problem and calculate its length.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br>