Math thinking question (urgent)

Question

The school sells baseball caps with the school logo on them to raise money for charity. Last year the

school sold 600 caps at $20 each, This year the school is planning to increase the price. A survey snows

that for every $2 increase, there will be a drop of 30 sales.

a) what should the selling price be to maximize the sales this year?

b) what is the maximum revenue from the caps?

Answer 1

(sales, price) =

(600, 20), (570, 22), (450, 30),

(0, 60), (630, 18), (660,16), (870, 2), (885, 1), (900, 0)

max sales of 900 with zero price or price = 1 cent

max revenue is when (450, 30) = (900/2, 60/2)

with price $30 and sales of 450 caps

max revenue = 30(450) = $13,500