You own the shoe store and are deciding which shoes to stock for upcoming season. You can either stock designer shoes, midrange shoes, or inexpensive shoes. If you stock designer shoes, you can stock either American designers or European designers. Based upon which shoes you stock, your profits will be as follows:
| Shoes |
Probability |
Profit ($'s) |
| American Designers |
0.2 |
|
100,000 |
| American Designers |
0.5 |
|
60,000 |
| American Designers |
0.3 |
|
-20,000 |
| European Designers |
0.1 |
|
150,000 |
| European Designers |
0.5 |
|
80,000 |
| European Designers |
0.4 |
|
-40,000 |
| Midrange |
0.4 |
|
60,000 |
| Midrange |
0.6 |
|
30,000 |
| Inexpensive |
0.3 |
|
50,000 |
| Inexpensive |
0.7 |
|
40,000
|
QUESTIONS:SHOW WORK
(For example, if you stock shoes by European Designers there is a 50% chance that your profits
will be $80,000.)
a) Use a decision tree to determine which shoes to stock in order to maximize expected profit.
b) Draw a risk profile for the optimal decision.
c) The probability of earning $50,000 when you stock inexpensive shoes is .3. How high
would this probability need to be for you to decide to stock inexpensive shoes?