what price per unit will yield a maximum total revenue?

Question

When a wholesaler sold a product at $30 per unit, sales were 288 units per week. After a price increase of $5, however, the average number of units sold dropped to 268 per week. Assuming that the demand function is linear, what price per unit will yield a maximum total revenue?

Answer 1

Let S = sales and P = price R=revenue

(288-268)/(30-35)=(S=288)/(P-30) => S=408-4P

R = S*P = =408P-4P²

dR/dP = 408 - 8P and the maximum will be at P=51.