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 $6,950 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.

1. Which location will yield the greatest profit if monthly demand is (1) 200 cars, (2) 300 cars?
2. At what volume of output will the two sites yield the same monthly profit?

Answer 1

1.

(1) Profit - Location B = $5500

(2) Profit - Location A = $11050

2.

x = 245 cars

Step-by-step explanation:

1.

Profit is the difference between the revenue and the total cost. To determine which location will provide greatest profit, we need to solve the equation for profit for both the locations under different demand scenarios as given in the question.

• Let Location A be the central city location.

• Let Location B be the outskirts locations

The profit equation for Location A = 90 * x - (6950 + 30 * x)

The profit equation for Location B = 90 * x - (4500 + 40 * x)

Where x is the monthly demand in number of cars.

Scenario (1) 200 Cars

Profit - Location A = 90 * 200 - (6950 + 30 * 200)

Profit - Location A = $5050

Profit - Location B = 90 * 200 - (4500 + 40 * 200)

Profit - Location B = $5500

Scenario (2) 300 Cars

Profit - Location A = 90 * 300 - (6950 + 30 * 300)

Profit - Location A = $11050

Profit - Location B = 90 * 300 - (4500 + 40 * 300)

Profit - Location B = $10500

2.

To calculate the output/ demand that will produce the same profit under both locations, we need to equate the two profit equations.

90 * x - (6950 + 30 * x) = 90 * x - (4500 + 40 * x)

90x - 30x - 6950 = 90x - 40x - 4500

60x - 6950 = 50x - 4500

60x - 50x = -4500 + 6950

10x = 2450

x = 2450 / 10

x = 245 cars