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 $4,400 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: (Click to select)OutsideCity yields the greatest profit.

300 cars: (Click to select)OutsideCity 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

a)

Profit = Revenue - Total costs

Revenue = Price x quantity sold

Total costs = Fixed costs + Variable costs

Profit at central city location when the monthly demand is 200 cars is calculated as

Profit = $ 90 x 200 cars - [ $6,940 +  $ 30 x 200 cars ]

Profit = $ 5,060

Profit at outside location when the monthly demand is 200 cars is calculated as

Profit = $ 90 x 200 - [ $ 4,400 + $40 x 200 cars ]

Profit = $ 5,600

Hence outside location  yields the greatest profit when the monthly demand is 200 cars.

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Profit at central city location when the monthly demand is 300 cars is calculated as

Profit = $ 90 x 300 cars - [ $6,940 +  $30 x 300 cars ]

Profit = $ 11,060

Profit at outside location when the monthly demand is 300 cars is calculated as

Profit = $ 90 x 300 - [ $ 4,400 + $40 x 300 cars ]

Profit = $ 10,600

Hence central city location  yields the greatest profit when the monthly demand is 300 cars.

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b)

Let Q be the volume of output that yields the same monthly profit

$ 90 x Q - [  $6,940 +  $ 30 x Q cars ] = $ 90 x Q - [ $ 4,400 + $ 40 Q ]

$90 Q - $ 6940 - 30Q = $ 90 Q - $ 4,400 - 40Q

$ 60 Q - $ 6940 = $ 50 Q - $ 4,400

$ 10 Q = $ 2,540

Q = $ 2,540 $ 10

Q = 254 cars

Volume of output = 254 cars

Thus at 254 cars volume of output the two sites will yield the same monthly profit.