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 $6,980 and labor, materials, and transportation costs of $30 per car. The outside location would have fixed monthly costs of $4,200 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: (City or Outside?) yields the greatest profit.
300 cars: (City or Outside?) 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

It is convenient to let a spreadsheet or graphing calculator do the math for this. Functions can be defined for cost and profit, and evaluated at each of the volumes of interest.

a1) For 200 cars, the Outside location yields the greatest profit

a2) For 300 cars, the City location yields the greatest profit

b) The sites yield the same profit for a volume of 278 cars.