question for math

Question

​Amy, the owner of​ Amy's Pottery, can produce china pitchers at a cost of

$4

each. She estimates the price function to be

p equals 18 minus 3 x=18−3x,

where p is the price at which exactly x pitchers will be sold per week. Find the number of pitchers that she should produce and the price that she should charge in order to maximize profit.​ Also, find the maximum profit.

How many pitchers should Amy produce to maximize​ profit?

Answer 1

The profit function is P(X) = x(18-3x)

= -3x^2 + 18x

the max occurs at -b/(2a) = -18/(-6) = 3

3*(18 - 3*3) = 3 * (18 - 9) = 3*9 = 27

She sells 3 pitchers for $9 each.

SHe will make $27