A) At 200 cars, the outskirts location will yield the greatest profit of $5,900, slightly higher than the central city location's profit of $5,040.
B) The two locations will yield the same monthly profit at a volume of output of 82 cars.
To determine which location will yield the greatest profit for different demand levels and calculate the break-even point, we have to compare the total costs and revenues for each location at each demand level.
A) Profit at 200 cars
Central City
Total Revenue = 200 cars * $90 per car = $18,000
Fixed Costs = $6,960
Variable Costs = 200 cars * $30 per car = $6,000
Total Costs = Fixed Costs + Variable Costs
= $6,960 + $6,000
= $12,960
Profit = Total Revenue - Total Costs
= $18,000 - $12,960
= $5,040
Outskirts
Total Revenue = 200 cars * $90 per car = $18,000
Fixed Costs = $4,100
Variable Costs = 200 cars * $40 per car = $8,000
Total Costs = Fixed Costs + Variable Costs
= $4,100 + $8,000
= $12,100
Profit = Total Revenue - Total Costs
= $18,000 - $12,100
= $5,900
Hence we can conclude that at 200 cars, the outskirts location will yield the greatest profit of $5,900, slightly higher than the central city location's profit of $5,040.
B) Break-even point
The break-even point is the output level where the total revenue equals the total costs, resulting in neither profit nor loss.
To find the break-even point, we set the total revenue equal to the total costs for both locations and solve for the number of cars (Q).
Central City
90Q = 6,960 + 30Q
60Q = 6,960
Q = 116
Outskirts
90Q = 4,100 + 40Q
50Q = 4,100
Q = 82
Hence, we can conclude that the two locations will yield the same monthly profit at a volume of output of 82 cars.
Full Question:
Although part of your question is missing, you might be referring to this full 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 $6,960 and labor, materials, and transportation costs of $30 per car. The outside location would have fixed monthly costs of $4,100 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:_yield the greatest profit. 300 cars:_yield the greatest profit.
B) At what volume of output will the two sites yield the same monthly profit?