A firm can produce 400 units per week. If its total cost function is C = 400 + 1000x dollars and its total revenue function is R = 1400x − x2 dollars.

Question

How many units, x, should it produce to maximize its profit?

x =  ____ units

Find the maximum profit.

$  ______

Answer 1

Profit = Revenue - Cost

1400x - x^2 - 400 - 1000x

-x^2 + 400x -400

take the derivative and set equal to zero

-2x + 400 = 0

x= 200 per week maximizes profit

-(200)^2 + 400(200) -400 = $40,000- $400 = $39,600 maximum profit per week