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 $ 7,000 and labor, materials, and transportation costs of $ 30 per car. The outside location would have fixed monthly costs of $ 4,700 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?
b. At what volume of output will the two sites yield the same monthly profit?