Problem 8-7 A retired auto mechanic hopes to open a rustproofing shop. Customers
ID: 355205 • Letter: P
Question
Problem 8-7 A retired auto mechanic hopes to open a rustproofing shop. Customers would be local new-car dealers. Two locations are being considered, one in the center of the city and one on the outskirts. The central city location would involve fixed monthly costs of $6,975 and labor, materials, and transportation costs of $30 per car. The outside location would have fixed monthly costs of $4,375 and labor, materials, and transportation costs of $38 per car. Dealer price at either location will be $99 per car. a. Which location will yield the greatest profit if monthly demand is (1) 340 cars? (2) 440 cars? 340 cars: (Click to select) yields the greatest profit. 440 cars: (Click to select)yields the greatest profit. b. At what volume of output will the two sites yield the same monthly profit? Volume of output casExplanation / Answer
For the central city location
For the outside location
a) If the volume of output (Q) = 340 cars,
Profit for central city location = Q(SP-VC) - FC = 340(99-30)-6975 = (340 x 69)-6975 = 23460-6975 = $16485
Profit for outside location = Q(SP-VC) - FC = 340(99-38)-4375 = (340 x 61)-4375 = 20740-4375 = $16365
So for 340 cars, the central city location yields the greatest profit
If the volume of output (Q) = 440 cars,
Profit for central city location = Q(SP-VC) - FC = 440(99-30)-6975 = (440x69) - 6975 = 30360-6975 = $23385
Profit for outside location = Q(SP-VC) - FC = 440(99-38)-4375 = (440x61) - 4375 = 26840-4375 = $22465
So for 440 cars, central city location yields the greatest profit.
b) let the volume of output = Q
Profit for central location = profit for outside location
=> Q(SP-VC) - FC = Q(SP-VC) - FC
=> Q(99-30)-6975 = Q(99-38)-4375
=> 69Q - 6975 = 61Q - 4375
=> 69Q-61Q = 6975-4375
=> 8Q = 2600
=> Q = 2600/8
=> Q = 325
So the volume of output at which the two sites yield the same profit is 325 cars.