Question: Question 1: John Smith owns a small firm that manufactures “Smith Sunglasses.” He has the opportunity to sell a particular seasonal model to Target. John offers Target two purchasing options:

Option 1: John offers to set his price at $65 and agrees to credit Target $50 for each unit Target returns to John at the end of the season (because those units did not sell). Since styles change each year, there is essentially no value in the returned merchandise.

Option 2: John offers a price of $53 for each unit, but returns are no longer accepted. In this case, Target throws out unsold units at the end of the season.

Assume (for simplicity) that this season’s demand for this model follows the following probability distribution. Target will sell those sunglasses for $100 each. John’s production cost is $25.

Probability Distribution of Demand for Smith Sunglasses

Demand Probability

80 0.10
100 0.10
120 0.15
140 0.20
160 0.20
180 0.15
200 0.10

a. How much would Target buy if they choose option 1?

b. How much would Target buy if they choose option 2?

c. Which option will Target choose? Why?

d. Suppose Target chooses option 1 and orders 140 units. What is John Smith’s expected profit?