Maximum profit? P=25-3x

Question

Amy, the owner of Amy's Pottery, can produce china pitchers at a cost of $5 each. She estimates the price function to be p=24-3x, 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.

Answer 1

Alexis,

 

For 1 pitcher cost is $5 and selling price is 25-3*1 = 22 so profit is $17

 

For 2 pitchers cost is $10 and selling price per pitcher is 25-3*2 = 19 so profit is 2*19 -10 = $28

 

For 3 pitchers cost is $15, selling price is 25-9 = 16 and profit is 3*16 - 15 = $33

 

For 4 pitchers cost is $20, selling price is 25-12 = 13 and profit is 4*13 - 20 = $32

 

For 5 pitchers cost is $25, selling price is 25-15 = 10 and profit is 5*10 - 25 = $25

 

So she should make and sell 3 pitchers for a profit of $33 

 

It can also be solved by system of equations but I think this is above mentioned is easier to understand.