Question

Suppose cost of production of a firm is given by:

TC=128+50Q-16Q^2+2Q^3

What amount of the product should be produced to maximize profit of the firm if price per unit output is 74? Find the maximum profit or loss.

Answer 1

Profit is maximized, when P = MC.

$MC = TC'(Q) = 50 - 32Q + 6Q^2 = 74.$

$3Q^2 - 16Q - 12 = 0,$

Q = (16 + 20)/6 = 6 units.

$TP = TR - TC = 74×6 - (128+50×6-16×6^2+2×6^3) = 160.$