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

Question

A firm can produce 200 units per week. If its total cost function is C = 600 + 1100x dollars and its total revenue function is R = 1300x − x² dollars, how many units, x, should it produce to maximize its profit?

x = ? units

Find the maximum profit

$ ?

Answer 1

Take the derivative of R-C and set equal to zero

(R-C)' = 1300 - 2x - 1100 = 0

2x =200

x = 200/2 = 100 units = profit maximizing output

Profit = R-C = 1300x -x^2 - 1100x -600

R(100)-C(100) = 1300(100) -(100)^2 -1100(100) -600

= 1300(100) -10000 -110000 -600

= 130,000 -10,000 - 110,000 -600

= $9,400 = maximum profit