Question

Suppose a company has fixed costs of $44,800 and variable cost per unit of 1 3 x + 222 dollars, where x is the total number of units produced. Suppose further that the selling price of its product is 1654 − 2 3 x dollars per unit.

Find break even

Fine max revenue

Answer 1

Price = 1654 - 23x

Total revenue (TR) = P.x = 1654x - 23x²

Total cost (TC) = FC + VC = FC + (AVC.x) = 44800 + x.(13x + 222) = 44800 + 13x² + 222x

Profit (Z) = TR - TC = 1654x - 23x² - 44800 - 13x² - 222x

Z = 1432x - 36x² - 44800

(1)

In break-even, Z = 0.

1432x - 36x² - 44800 = 0

36x² - 1432x + 44800 = 0

Solving this quadratic equation using online solver, both the roots come out as Imaginary numbers. So break-even solution does not exist.**

(2)

Revenue is maximized when dTR/dx = 0

dTR/dx = 1654 - 46x = 0

46x = 1654

x = 35.96

P = 1654 - (23 x 35.96) = 1654 - 827.08 = 826.92

Maximum revenue = P.x = 826.92 x 35.96 = 29,736.04

**Please cross-check the numbers and AVC/Price function you have provided.