A retired auto mechanic hopes to open a rustproofing shop. Customers would be local deal* ers. Two locations are being considered, one in the centre of the city and one in the outskirts. The central city location would involve fixed monthly cost of $7,000 and labour, materials, and transportation costs of $30 per car. The outskirt location would have fixed monthly costs of $4,700 and labour, materials, and transportation costs of $40 per car. Price at either location will be $90 per car.
a. Which location will yield the greatest profit if monthly demand is (i) 200 cars? (ii) 250 cars?
b. At what quantity of cars will the two sites yield the same monthly profit?