9599
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<mdoxml version="1.0"><mdo:image alt="seaside locations" src="seaside-smaller.png" style="width: 300px; height: 259px; margin-right: 0px; margin-left: 10px; float: right;"></mdo:image><br></br>
<div class="framework" style="">Luigi plans to set up a new icecream business by the seaside. But where should he set up his first stall?<br></br>
<br></br>
If he sets up shop at the Beach Cafe (A), the weather won't matter. On the other hand, if he puts his stall on the beach (D), he'll do much better if it's sunny, but much worse if it rains. <br></br>
He could go for the bandstand (B) or the beach umbrella (C) instead ...<br></br>
<br></br>
What should he do?</div>
<p><br></br>
<br></br>
You can model Luigi's options using yellow cubes for sunny days and blue cubes for rainy days.<br></br>
<br></br>
Put two blue and two yellow cubes in a bag so that the colour of the cubes cannot be seen. </p>
<br></br>
Now decide where Luigi should put his first icecream stall. The table tells you how many credits he can expect to make per day in each location:<br></br>
<br></br>
<table style="border-spacing: 1px; width: 70%;" border="1">
<thead>
<tr>
<th scope="row" style=""> </th>
<th scope="col" style="">Rain (blue)</th>
<th scope="col" style="">Sunny (yellow)</th>
</tr>
</thead>
<tbody>
<tr>
<th scope="row" style="text-align: left;">Beach cafe, A</th>
<td style="text-align: center;padding:1px;padding:1px;padding:2px;">25</td>
<td style="text-align: center;padding:1px;padding:1px;padding:2px;">25</td>
</tr>
<tr>
<th scope="row" style="text-align: left;">Bandstand, B</th>
<td style="text-align: center;padding:1px;padding:1px;padding:2px;">22</td>
<td style="text-align: center;padding:1px;padding:1px;padding:2px;">42</td>
</tr>
<tr>
<th scope="row" style="text-align: left;">Umbrella, C</th>
<td style="text-align: center;padding:1px;padding:1px;padding:2px;">19</td>
<td style="text-align: center;padding:1px;padding:1px;padding:2px;">49</td>
</tr>
<tr>
<th scope="row" style="text-align: left;">Beach, D</th>
<td style="text-align: center;padding:1px;padding:1px;padding:2px;">16</td>
<td style="text-align: center;padding:1px;padding:1px;padding:2px;">66</td>
</tr>
</tbody>
</table>
<br></br>
Now pick a cube How many credits did Luigi make?<br></br>
<ul>
<li>Was this a wise choice?</li>
<li>If you were to choose again, would you stick with the same option or change to another? </li>
<li>If you would not change, why not?</li>
<li>If you would change, which would you choose and why?</li>
<li>Which would be Luigi's best option over a month?</li>
<li>Why?</li>
<li>See if experiment confirms what you expect.</li>
<li>Did the experiment confirm what you expected?</li>
<li>If not, why do you think that was?</li>
<li>Would that be his best option over a 6 month season?</li>
<li>What assumptions have we made in this model? </li>
</ul>
<h3>Luigi opens a second icecream stall!</h3>
<br></br>
Business is doing quite well, so Luigi decides to invest in another icecream stall further round the beach, where it won't compete with his first stall, and where there are likely to be many more people.<br></br>
<br></br>
There are three locations he thinks might do: on the beach (X), under an umbrella in front of the pier (Y), or in a cafe at the end of the pier (Z). However, Big Frankie is in charge here, and Luigi will have to pay him rent.<br></br>
<br></br>
The table gives the daily rent and the number of credits he can expect to make per day.<br></br>
<br></br>
<table style="border-spacing: 1px; width: 80%;" border="1">
<thead>
<tr>
<th scope="row"> </th>
<th scope="row">Rent</th>
<th scope="col">Rain (blue)</th>
<th scope="col">Sunny (yellow)</th>
</tr>
</thead>
<tbody>
<tr>
<th scope="row" style="text-align: left;">Beach (X)</th>
<td style="text-align: center;padding:1px;padding:2px;">15</td>
<td style="text-align: center;padding:1px;padding:2px;">-40</td>
<td style="text-align: center;padding:1px;padding:2px;">280</td>
</tr>
<tr>
<th scope="row" style="text-align: left;">In front of the pier (Y)</th>
<td style="text-align: center;padding:1px;padding:2px;">20</td>
<td style="text-align: center;padding:1px;padding:2px;">120</td>
<td style="text-align: center;padding:1px;padding:2px;">200</td>
</tr>
<tr>
<th scope="row" style="text-align: left;">Cafe at the end of the pier (Z)</th>
<td style="text-align: center;padding:1px;padding:2px;">100</td>
<td style="text-align: center;padding:1px;padding:2px;">-120</td>
<td style="text-align: center;padding:1px;padding:2px;">600</td>
</tr>
</tbody>
</table>
<br></br>
<br></br>
This time, we are going to make the model a little more sophisticated. Luigi lives in an area where a rainy day is as likely as a sunny day. However, if it is sunny one day, it is more likely to be sunny the following day, and if it is rainy one day, the next day is more likely to be wet.<br></br>
<br></br>
For the first day, put two yellow and two blue cubes in the bag. Take one out and keep it.<br></br>
<ul>
<li>If it is yellow (so this was a sunny day), remove one of the blue cubes from the bag and add two more yellow ones - you should now have three yellow cubes and one blue cube in your bag.</li>
<li>If the first cube is blue (a rainy day), remove one of the yellow cubes from the bag and add two more blue ones - this time you should have three blue cubes and one yellow cube in your bag.</li>
</ul>
Without looking at the cubes, take a second one out of the bag.<br></br>
<br></br>
Decide which option you think Luigi should go for, then use the cubes to see how he might do on two consecutive days.<br></br>
<ul>
<li>If you were to choose again, would you stick with the same option or change to another?</li>
<li>If you would not change, why not?</li>
<li>If you would change, which would you choose and why?</li>
<li>Which would be Luigi's best option over a month?<br></br>
Why?</li>
<li>See if experiment confirms what you expect.</li>
<li>Did the experiment confirm what you expected?</li>
<li>If not, why do you think that was?</li>
<li>Would that be his best option over a 6 month season?</li>
<li>How realistic do you think this model is? Could you improve it?</li>
</ul>
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Luigi's Icecream Business
Where should Luigi set up his stall? Should he go for the safer options, hoping to limit his losses, or would be better off with a riskier strategy, focusing on maximising his profit?
jag55
work in progress
jag55
Probability - modelling approach