Nordic Inc. has designed four ski boot styles it plans to sell in the next winter season: Terrain, Blizzard, IceFix, and Freezdom. Nordic can produce some ski boot styles well in advance of the selling season, with the remaining styles produced after the next Ski E lite Athletes Trade (SEAT) show that occurs before the selling season. At the time it makes its initial production decision, Nordic's forecast for each boot's demand is normally distributed with means and standard deviations listed in the table below. The table also lists results from the newsvendor model when expected profit is maximized.
|
Boot
|
Price
|
Mean
|
Std. Dev
|
Cp
|
Ce
|
Q
|
Expected Newsvendor Profit
|
|
Terrain
|
200
|
100
|
30
|
10
|
48
|
120
|
4190
|
|
Blizzard
|
150
|
150
|
50
|
20
|
60
|
184
|
7730
|
|
IceFix
|
120
|
200
|
70
|
9.6
|
28.8
|
248
|
4906
|
|
Freezdom
|
100
|
300
|
50
|
8
|
24
|
334
|
6692
|
After the trade show, and before it makes its final production decision, Nordic will know exact demand for each boot.
a. What is Nordic's expected profit if Nordic chooses to produce all four boot styles before the SEAT show?
b. What is Nordic's expected profit if Nordic chooses to produce every boot style after the SEAT show (and assuming that all of its production arrives by the start of the selling season)?
c. Because the SEAT show concludes shortly before the selling season, Nordic has limited capacity for production after the show. As a result, it needs to produce at least 300 pairs of boots before the show. Recall, each boot style is produced either before or after the show (i.e., no style is produced both before and after the show). How many pairs of boots should Nordic produce before the SEAT show?