1. LEGO’s product designers have designed a new kit to celebrate the upcoming European football championship. The kit costs $22.50 to produce (including shipping to stores), and LEGO will sell them for $50 in retail stores. Unfortunately the production lead time is half a year, so LEGO must commit to production now, well before demand is known, in order to have items on the shelves in time for the football championship. LEGO estimates the demand will be 120000 kits with a standard deviation of 50000. Kits left over after the championship will be sold at the discounted price of $15.

(a) (5pts) Assume that LEGO chooses to produce 150000 kits. What is the probability that LEGO will run out of kits during the championships? What is LEGO’s expected profit on the football kits?

(b) (5pts) How many LEGO kits will be sold, on average? Explain why this quantity is less than the average demand of 120000.

(c) (5pts) Now assume that LEGO is trying to maximize its expected profit. How many kits should be produced and what is the expected profit?

(d) (5pts) Now suppose that the $22.50 selling price includes a $5 per kit licensing fee payable to the UEFA (European football association) for every kit produced by LEGO. Assuming that LEGO produces the number of kits you found in (c), what is UEFA’s licensing revenue?

(e) (5pts) Assuming LEGO will produce the number of kits that maximizes its profit, what is the licensing fee (in $ per kit) that UEFA should charge to maximize its licensing revenue? What is LEGO’s expected profit in this arrangement, and what is UEFA’s licensing revenue?

(f) (5pts) Assuming that LEGO and UEFA want to maximize the sum of LEGO and UEFA’s profit, find the number of kits that should be produced by LEGO and the resulting supply chain profit.

(g) (10pts) Suggest a contractual arrangement between LEGO and UEFA that maximizes the profit plus licensing revenue, while giving both LEGO and UEFA more profit than they received in part (c) and (d).