QUESTION $2$

Mathabatha is thinking about opening a shop in his hometown, he would like to take his own bike on $80-$mile trips with his friends, but he believes that any small business should be started only if there is a good chance of making a profit. He can open a small shop, a large shop, or no shop at all. The profits will depend on the size of the shop and whether the market is favorable or unfavorable for his products. Because there will be a $10-$year lease on the building that he is thinking about using, he wants to make sure that he makes the correct decision. He is also thinking about hiring his old marketing Lecturer to conduct a marketing research study. If the study is conducted, the study could be favorable $($i$.$e$.,$ predicting a favorable market$)$ or unfavorable $($i$.$e$.,$ predicting an unfavorable market$).$

He has done some analysis about the profitability of the shop. If he builds the large bicycle shop, he will earn $R600,000$ if the market is favorable, but he will lose $R400,000$ if the market is unfavorable. The small shop will return a $R350,000$ profit in a favorable market and a R$150,000$ loss in an unfavorable market. At the present time, he believes that there is a $55\%$ chance that the market will be favorable. His old marketing lecturer will charge him $R50,000$ for the marketing research. It is estimated that there is a $0\mathrm{.}65$ probability that the survey will be favorable. Furthermore, there is a $0\mathrm{.}85$ probability that the market will be favorable given a favorable outcome from the study. However, the marketing lecturer has warned Mathabatha that there is only a probability of $0\mathrm{.}11$ of a favorable market if the marketing research results are not favorable. Now Mathabatha is confused.

What should Mathabatha do$?($Make use of a decision tree and show all the steps$).$

$[30]$