Question

A donut shop is going to sell donuts for a price P that is no less than 60 pence and no more than 150 pence. The shop determines that the number of donuts that it will sell is given by the following formula: 750 – 5P. What price should the shop charge to maximise revenue?

Answer 1

$60 \leqslant P \leqslant150$

total revenue for selling $750-5P donuts\, \text{is} (750 -5P)P=750P-5P^{2}$

for maximum $\frac{d}{dP}(750P-5P^{2})=0$

$750 - 10P=0$

$P= 750/10 = 75$

The shop should charge $75 pence$ per donut so that maximum revenue $=750\times 75 - 5\times 75^{2} = 28125 pence$