amy, the owner of amy's pottery, can produce china pitchers at a cost of $ 3 each. she estimates the price function to be p equals 20 minus 4 x comma 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.

Amy should produce 2 pitchers to maximize profit and the maximum profit will be $18.

Step-by-step explanation:

Amy can produce china pitchers at a cost of $3 each.

She estimates the price function that can be represented by

p = 20 - 4x

Let she sells the number of x pitchers in a week.

Then the selling price of x pitchers will be = $x(20 - 4x)

Cost price of x pitchers = $3x

Profit (P) = Selling price - Cost price

              = x(20 - 4x) - 3x

              = 20x - 4x²- 3x

              = 17x - 4x²

To maximize the profit,

P' = 17 - 8x = 0

8x = 17

x = 2.125

x ≈ 2

Therefore, 2 pitchers should be produced.

Profit = 17x - 4x²

         = 17(2) - 4(2)²

         = 34 - 16

         = $18

to find the perimeter of the rectangle this is the expression:

x-9+x-9+3x-4+3x-4=138

if we simplify it:

8x-26=138

remember, 138 is what it all adds up to

the length is 11.5cm

the width is 57.5cm

the area is 661.25cm^2

the answers might not be correct use at own risk