A department store has 700 pairs of purple capri stretch pants that it must sell in the next four weeks. The store manager knows that demand by week for the next four weeks will be linear, with the following price-response functions:

Week 1: d1(p1) = 1,000 – 100p1 Week 2: d2(p2) = 800 – 100p2 Week 3: d3(p3) = 700 – 100p3 Week 4: d4(p4) = 600 – 100p4 Assume that the demands in the different weeks are independent—that is, that customers who do not buy in a given week do not come back in subsequent weeks.

a. What is the optimum price the retailer should charge per pair if he can only set one price for all four weeks? What is the corresponding revenue?

b. Assume he can charge a different price each week. What are the optimum prices by week he should charge? What is the corresponding revenue?