Your neighbours operate a successful bake shop. One of their specialties is a very rich whipped-cream-covered cake. They buy the

Question

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?

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