In the complementary-product pricing model in Example 7.3, we have assumed that the profit per unit from shirts and ties is given. Presumably this is because the prices of these products have already been set. Change the model so that the company must determine the prices of shirts and ties, as well the price of suits. Assume that the unit costs of shirts and ties are, respectively, $20 and $15. Continue to assume that, on average, 2 shirts and 1.5 ties are sold along with every suit (regardless of the prices of shirts and ties), but that shirts and ties have their own separate demand functions. These demands are for shirts and ties purchased separately from suit purchases. Assume constant elasticity demand functions for shirts and ties with parameters 288,500 and -1.7 (shirts), and 75,460 and -1.6 (ties). Assume the same unit cost and demand function for suits as in Example 7.3.
a. How much should the company charge for suits, shirts, and ties to maximize the profit from all three products?
b. The assumption that customers will always buy, on average, the same number of shirts and ties per suit purchase, regardless of the prices of shirts and ties, is not very realistic. How might you change this assumption, and change your model from part a accordingly, to make it more realistic?