Maximizing Profits Problem Help?

Question

Can someone tell me what formula I should use to solve this problem:

Suppose a company has fixed costs of ($27,200 ) and variable costs of (2/5x + 222 ) dollars per unit, where x is the total number of units produced. Suppose further that the selling price of its product is (1300 - 3/5x ) dollars per unit. Determine the price when profit is maximized.

Any help would be appreciated!!!

Answer 1

Total costs = 27,200 + x(0.4x + 222)

Total Revenue = x(1300 - 0.6x)

Profit = x(1300 - 0.6x) - [27,200 + x(0.4x + 222)]

Profit = 1078x - x^2 - 27,200

dProfit/dx = 1078 - 2x = 0

x = 539 units

You get the maximum profit selling 539 units.

Price(539 units) = 1300 - 0.6*539 = $976.60