Question

A large wood products company is negotiating a contract to sell plywood overseas. The fixed cost that can be allocated to the production of plywood is $800,000 per month. The variable cost per thousand board feet is $155.50. The price charged will be determined by p = $600 − (0.05)D per 1,000 board feet.
For this situation, determine the optimal monthly sales volume for this product and calculate the profit (or loss) at the optimal volume.

Answer 1

The profit is maximized, when such quantity Q is produced, for which MR = MC.

MR = TR'(Q) = (P×Q)' = 600 - 0.1Q,

MC = TC'(Q) = (800,000 + 155.5Q)' = 155.5.

600 - 0.1Q = 155.5,

0.1Q = 444.5,

Q = 4,445 units.

P = 600 - 0.05×4,445 = $377.75.

Total profit is TP = TR - TC = 377.75×4,445 - (800,000 + 155.5×4,445) = $187,901.25.