Optimal Retail Price
calculus: profit optimization?
okay so the terrible question is…
your neighbours operate a bakery. They buy cakes from a supplier who charges $6/cake, and they sell 200 cakes weekly at $10 each. Research shows that profit from the cake sales can be increased by increasing the price. Unfortunately, for every increase of $0.50, sales will drop by seven cakes.
a) what is the optimal retail price for a cake to obtain a maximum weekly profit?
(p – 10)/(q – 200) = 0.5/-7
(p – 10)(-7/0.5) = q – 200
q = -14p + 140 + 200
q = -14p + 340
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