A firm has monthly average costs in dollars given by C 4400

A firm has monthly average costs, in dollars, given by C = 44,000/x + 300 + x where x is the number of units produced per month. The firm can sell its product in a competitive market for $2100 per unit. If production is limited to 250 units per month, find the number of units that gives maximum profit. x = units Find the maximum profit. $

Solution

C = (44000/x) + 300 + x

For maximum profit, dC/dx = 0 ========> (-44000/x²) + 1 = 0 =======> x = 209.8

b) Maximum profit = (44000/209.8) + 300 + 209.8 = 719.5