The owner of a ski apparel store in Winter Park, Colorado, must make a decision in July regarding the number of ski jackets to order for the following ski season. Each ski jacket costs $54 each and can be sold during the ski season for $145. Any unsold jackets at the end of the season are sold for $45. The demand for jackets is expected to follow a Poisson distribution with a average rate of 80. The store owner can order jackets in lot sizes of 10 units.
a. How many jackets should the store owner order if she wants to maximize her expected profit?
b. What are the best-case and worst-case outcomes the owner may face on this product if she implements your suggestion?
c. How likely is it that the store owner will make at least $7,000 if she implements your suggestion?
d. How likely is it that the store owner will make between $6,000 to $7,000 if she implements your suggestion?