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 location would involve fixed monthly costs of $7,000 and labor, materials and transporation cost $30 per car. The outside location would have fixed monthly cost of $4,700 and labor materials, and transporation cost of $40 per car. Dealer price at either location will be $90 per car
which location will yield the greatest profit if monthly demand is (1) 200 cars ? (2) 300 cars?

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

Answer 1

Answer:

1) Outside Location

2) Central Location

The profit will be the same when monthly demand is 230 cars

Explanation:

Let central location be termed as location A

Let outside location be termed as location B

1. Demand 200 cars

Profit- Location A = (90-30) * 200 - 7000 = $5000

Profit- Location B = (90-40) * 200 - 4700 =$5300

2. Demand 300 cars

Profit- Location A = (90-30) * 300 - 7000 = $11000

Let x be the number of cars where profit is same,

we will equate both the profit equations

(90-30)*x - 7000 = (90-40)*x - 4700

60x - 7000 = 50x - 4700

60x - 50x = 7000 -4700

10x = 2300

x = 2300/10

x = 230 cars

Profit- Location B = (90-40) * 300 - 4700 =$10300