Question

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 $6,940 and labor, materials, and transportation costs of $30 per car. The outside location would have fixed monthly costs of $4,500 and labor, materials, and transportation costs of $40 per car. Dealer price at either location will be $90 per car. a. Which location will yield the greatest profit if monthly demand is (1) 200 cars? (2) 300 cars? 200 cars: yields the greatest profit. 300 cars: yields the greatest profit. b. At what volume of output will the two sites yield the same monthly profit? Volume of output cars

Answer 1

Let total profit = y

Number of cars = x

total profit = earnings - fixed cost - variable cost

For center of the city:

y = 90*x - 6940 - 30*x

y = 60*x - 6940         .....(1)

For Outside location:

y = 90*x - 4500 - 40*x

y = 50*x - 4500       ......(2)

First part: (1) if there are 200 cars

x = 200, Put the value of x in eq. (1) and (2) we will get:

For central location y = 5060

For outside location y = 5500

thus outside location gives greatest profits.

(2) If number off cars is 300

x = 300, Put the value of x in eq. (1) and (2) we will get:

For central location y = 11060

For outside location y = 10500

thus central location gives greatest profits.

Part b. To find the number of cars where the two sides will yeild the same monthly profits find the value of x from eq. (1) and (2).

y = 60*x - 6940         .....(1)

y = 50*x - 4500       ......(2)

Put value of y from eq(1) to eq(2)

60*x - 6940 = 50*x - 4500

this gives x = 244

Thus at 244 number of cars the profits from the two locations will be same.