11. Your neighbours operate a successful bake shop. One of their specialties is a very

rich whipped-cream-covered cake. They buy the cakes from a supplier who

charges $6.00 per cake, and they sell 200 cakes weekly at $10.00 each. Research

shows that profit from the cake sales can be increased by increasing the price.

Unfortunately, for every increase of $0.50 cents, sales will drop by seven cakes.

a. What is the optimal retail price for a cake to obtain a maximum weekly

profit?

b. The supplier, unhappy with reduced sales, informs the owners that if they

purchase fewer than 165 cakes weekly, the cost per cake will increase to

$7.50. Now what is the optimal retail price per cake, and what is the bake

shop's total weekly profit?

c. Situations like this occur regularly in retail trade. Discuss the implications

of reduced sales with increased total profit versus greater sales with

smaller profits. For example, a drop in the number of customers could

mean fewer sales of associated products.