Question

A company produces a walkie-talkie communications device for use in industrial settings. The fixed cost (CF) is $90,000 per month, and the variable cost (cV) is 115 per unit. The selling price per unit is p = $195 – 0.033(D), in which D is the demand or number of units sold. Determine the optimal volume for this product; that is, the value of demand D at which profit is maximized. (Enter your answer as a number without any units.)

Answer 1

Total Cost(TC) = Fixed Cost + Total Variable cost

Here, Fixed Cost = 90,000 and Total Variable cost = Variable cost per unit*Quantity = 115D

=> Total Cost(TC) = 90,000 + 115D

Total Revenue(TR) = p*D = (195 – 0.033(D))*D

In order to maximize profit a firm produces that quantity at which MR = MC where MR = Marginal Revenue = d(TR)/dQ = 195 - 2*0.033D and MC = Marginal cost = d(TC)/dQ = 115

Thus MR = MC => 195 - 2*0.033D = 115 => D = 1212.12

Hence, the value of demand D at which profit is maximized is D = 1212.12 (or 1212 approx)