Question $12.$

Carla would like to open a small dress shop. At the present time, she believes that the chances of a successful or unsuccessful dress shop are about the same $(50\%).$ If Carla opens a shop and it is successful, she expects to make a profit of $$100,000.$ If she opens a shop that proves to be unsuccessful she will lose $$50,000.$ On the other hand, if Carla chose not to open her own shop, she would have the option of investing in a dress shop being started by her best friend Amanda. The probabilities of Amanda's shop being successful are the same as Carla's. Carla would only stand to make $$40,000$ if the shop was successful but if it was unsuccessful she would only lose $$30,000.$ Of course Carla can always do nothing.

a$-$ Draw a decision tree for this problem. What is Carla's best strategy?

b$-$ Draw the risk profiles and cumulative risk profiles for the problem

c$-$ Is there any kind of dominance among the possible alternative decisions? Explain.

d$-$ After a second thought Carla realizes that the profit she can make from her own shop is not strictly $$100,000$ but it can be as low as $$90,000$ and as high as $$110,000.$ Also, her profit from Amanda's shop will be varying in the range $[20,000,60,000].$ Perform $2-$way sensitivity analysis and draw a graph to identify the conditions under which either of the two alternatives is preferred.