Jill Kuo owns a small firm that manufactures “Chilly Jilly” wraps for women; the tag line of the company is “Wraps in a bag—use as a shawl, scarf or sarong.” Jill has the opportunity to sell a particular seasonal design through the catalog retailer Land’s End. The season’s demand for this design is forecasted to be normally distributed, with a mean of 10,000 and a standard deviation of 4,000. Land’s End will sell those wraps for $100 each. Jill’s production cost is $25 per wrap. She sets her wholesale price at $60. Styles change each year, so there is no value in the unsold merchandise.

Jill decides to take back unsold merchandise from Land’s End at the end of the season for a fixed buyback price. (Recall that styles change each year, so there is no value in the returned merchandise.) What should be the buyback price in order to maximize the total profit of the supply chain?

What is Jill’s expected profit if the buyback price in part A is used?