Urgent question :)

Question

The cost, in cents, to produce x cups of Mountain Thunder Lemonade at Junior's Lemonade Stand is C(x) = 6x + 80, x > 0 and the price-demand function, in cents per cup, is p(x) = 30 - x, 0 ≤ x ≤ 20. • Construct the profit function P(x). • Find the number of items to be sold (x) to maximize profit. • Find the maximum profit. • What should be the price per item to obtain maximum profit?

Answer 1

R(x) = px = 30x -x^2

Profit = R -C = 30x -x^2 -6x -80 = 24x -x^2 -80

R' -C'= 24-2x=0

x=24/2 =12= profit maximizing output

max profit = 24(12)-12^2 -80= 144-80= 64 cents