Spectrum brands manufactures and sells George Foreman grills through Target stores we will consider the contracting problem between Spectrum and Target in this problem. Consider a specific grill, the 6-serving removable plate & panini grill with digital temperature, that retails for $100.00 (I.e., the end-customers pay this price at target stores). Spectrum’s manufacturing cost for the grill, including the distribution cost, is $25.00. The barbecue grills are seasonal products with almost all of the annual sales taking place between late-spring and late-summer. Any leftover at the end of the summer is salvaged to free up space in retail store for winter items. Spectrum offers Target two purchasing options.

Contract 1 (buyback contract). Spectrum offers to set the wholesale price at $65 per grill (i.e., Target will pay this price to spectrum) and agrees to credit Target $53 for each unit Target returns to Spectrum at the end of the season (because those units did not sell). Since models/features of the grills change every year, there is no value in returned merchandise, and are donated.

Contract 2 (no-returns contract). Spectrum offers a wholesale price of $55 for each unit to Target, but returns are no longer accepted. In this case, Target donates the unsold grills at the end of the season (with no financial benefit)

The season’s demand is normally distributed with mean of 200 and standard deviation of 125.

A) How much would Target buy if it choses contract 1?

B) How much would Target buy if it choses contract 2?

C) Which option would target choose? Support your recommendation with calculations.

D) Suppose Target chooses option 1 and orders 275units. What is Spectrum’s expected profit?