A firm sells five women's ski parkas. Some data on those parkas are listed below:
|
Parka
|
Price
|
μ
|
σ
|
C0
|
Cu
|
Q
|
Expected Profit
|
|
A
|
$220
|
1,000
|
300
|
35.2
|
52.8
|
1,202
|
$41,740
|
|
B
|
205
|
2,000
|
800
|
28.7
|
49.2
|
2,540
|
73,618
|
|
C
|
190
|
3,000
|
1500
|
22.8
|
45.6
|
4,012
|
98,429
|
|
D
|
175
|
2,000
|
1200
|
17.5
|
42.0
|
2,809
|
59,186
|
|
E
|
160
|
1,000
|
700
|
12.8
|
38.4
|
1,472
|
27,011
|
Q in the above table is the optimal newsvendor quantity and "Expected Profit" is the news-vendor expected profit if Q is ordered. The firm will produce some parkas well in advance of the selling season. The other parkas are produced after a trade show that occurs shortly before the season starts. After attending the trade show, the firm will basically know demand for each parka. Unfortunately, the firm's capacity is limited after the trade show, so the firm wants to produce at least 5,000 parkas before the trade show. Furthermore, a parka should be produced either before the trade show or after the trade show, but a parka should not be produced in both production opportunities.
a. What is the firm's expected profit if every parka is produced before the trade show?
b. What is the firm's expected profit if every parka is produced after the trade show?
c. What should the production quantities before the trade show be for each parka?
d. What is the expected number of units the firm will produce after the trade show? (Assume that there is sufficient after-trade show capacity given the before-trade show order.)
e. What is the firm's expected profit?