Question

A factory manager is planning for the manufacture of plywood to be sold overseas. The fixed cost of operation is estimated at $800,000 per month while the variable cost is $155 per thousand board feet of plywood. The selling price will depend on how much will be produced and sold and is determined by the relationship, price per thousand board feet, p = $600-0.05D, where D is the amount produced and sold in thousands of board feet. Determine the monthly production that will maximize the total revenue and calculate the corresponding total profit per month. Determine also the corresponding average production cost per thousand board feet of plywood at this level of production. For maximum revenue, 6000 (to the nearest unit) thousands of board feet per month must be produced and the corresponding monthly proft is equal tRound to the nearest dollar.) At this production level, the price per thousand board feet is (Round to the nearest cent), and The average cost of production per thousand board feet is S 288.33 (Round to the nearest cent)

Answer 1

P = 600 - .05 Q, FC = 800,000, MC = 155 TR = P.Q = 600 Q - .05Q^2 partial differential TR/partial differential Q rightwardsdoublearrow 600 - .05 times 2 Q = 0, thus Q* = 600 times 100/2 times .05 = 60000/10 So at Q* = 6000 units Total pi (at Q = 6000) = P.Q - FC - TVC TVC rightarrow total variable cos t = MC middot Q = [600 - .05 times 6000/100] times 6000 - 900, 000 - 155 times 6000 = [600 - 300] times 6000 - 800,000 - 930,000 = 1800 000 - 800,000 - 930,000 = 70,000 $ P = 300 $ = 600 - .05 times 6000 Ac of prod^n = TC/Q = 800,000 + 155 times 6000/6000 = 288.33 $