1. Doc Nix Productions sells specialty T-Shirts that are sold at a single basketball game each. Doc Nix is trying to decide how many to buy for an upcoming game. During the game itself, which lasts one evening, Doc can sell T-Shirts for $11 apiece. However, when the game ends unsold T-shirts have no value. Due to a licensing agreement, Doc needs to make sure that leftover shirts are destroyed using a method that ends up costing $0.25 for each unsold T-Shirt. It costs Doc $7.50 to buy a specialty T-Shirt from the supplier. The supplier he uses has a cost per shirt of $3. Doc estimates that demand is distributed as shown below. Doc's supplier is contemplating "cutting out the middleman" (i.e., Doc Nix) and offering its products only through a direct channel.. In this case, please answer the following: What is the supplier's expected profit?How many specialty T-Shirts should the supplier produce to maximize profits? Doc's supplier is also considering offering him a buyback contract with the same wholesale price. What is the optimal buyback amount (i.e., b)?What is Doc's expected profit with the buyback contract?What is the supplier's expected profit with the buyback contract?

Demand	325	350	375	400	425	450
Probability	0.10	0.15	0.10	0.20	0.25	0.20