Consider a manufacturer selling DVDs to a retailer for $6 per DVD. The production cost of each DVD is $1 and the retailer prices each DVD at $10. Retail demand for DVDs is normally distributed, with a mean of 1,000 and standard deviation of 300. The manufacturer has offered the retailer a quantity flexibility contract with α = β = 0.2. The retailer places an order for 1,000 units. Assume that salvage value is zero for both the retailer and the manufacturer.
a. What is the expected profit for the retailer and manufacturer?
b. How much will profit increase for the retailer if α increases to 0.5?

c. How much will profit increase for the retailer if β increases to 0.5 (keeping α at 0.2)?