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 $6,950 and labor, materials, and transportation costs of $30 per car. The outside location would have fixed monthly costs of $4,350 and labor, materials, and transportation costs of $38 per car. Dealer price at either location will be $98 per car.

a. Which location will yield the greatest profit if monthly demand is (1) 330 cars? (2) 430 cars? 330 cars: yields the greatest profit. 430 cars: yields the greatest profit.

b. At what volume of output will the two sites yield the same monthly profit?

X = 325 cars will yield same profit in both locations

Explanation:

Location City Outskirts

Dealer Price $ $

(98 x 330) 32340 32340

Labour, Material

and Transportation Cost

($30/car x 330 cars) (9900)

($38/car x 330 cars) (12540)

Fixed Cost (6950) (4350)

Profit 15,490 15450

City will yield greatest profit if monthly demand is 330 cars

Location City Outskirts

Dealer Price $ $

(98 x 430) 42,140 42,140

Labour, Material

and Transportation Cost

($30/car x 430 cars) (12900)

($38/car x 430 cars) (16340)

Fixed Cost (6950) (4350)

Profit 22,290 21450

City will yield greatest profit if monthly demand is 430 cars

b)

let X be the volume of output for both sites to yield same profit

City

Dealer Price = 98X

Labour, material and transportation = 30X

Fixed cost = 6950

Profit = 98X - (30X+6950)

Outskirts

Dealer Price = 98X

Labour, Material and transportation = 38X

Fixed Cost = 4350

Profit = 98X - (38X+4350)

Both Profits are same therefore

98X-30X-6950 = 98X-38X - 4350

-30X+38X = - 4350+6950

-8X = 2600

X = 325 cars will yield same profit in both locations