Question

Frank's Pasta Maker has fixed operating costs of $28,500. The company's one product sells for $60 per unit while variable operating costs are $45 per unit. At what quantity of sales are all fixed and variable operating costs covered?

a. 1,634 units
b. 1,900 units
c. 475 units
d. 1,465 units

Answer 1

The profit-maximizing quantity of output for Frank's Pasta Maker is 3 units, covering all fixed and variable operating costs. The correct answer is c. 475 units.

Step-by-step explanation:

The profit-maximizing quantity of output can be determined by finding the level of output where total revenue equals total cost. To find this quantity, we need to calculate the total revenue and total cost for each level of output and compare them.

Let's calculate the total cost for each output level:

1. For 1 unit, the variable cost is $45, so the total cost is $28,500 + $45 = $28,545
2. For 2 units, the variable cost is 2 * $45 = $90, so the total cost is $28,500 + $90 = $28,590
3. For 3 units, the variable cost is 3 * $45 = $135, so the total cost is $28,500 + $135 = $28,635
4. For 4 units, the variable cost is 4 * $45 = $180, so the total cost is $28,500 + $180 = $28,680
5. For 5 units, the variable cost is 5 * $45 = $225, so the total cost is $28,500 + $225 = $28,725

Now, let's calculate the total revenue for each output level:

1. For 1 unit, the total revenue is 1 * $60 = $60
2. For 2 units, the total revenue is 2 * $60 = $120
3. For 3 units, the total revenue is 3 * $60 = $180
4. For 4 units, the total revenue is 4 * $60 = $240
5. For 5 units, the total revenue is 5 * $60 = $300

Finally, let's compare the total revenue and total cost for each level of output:

1. For 1 unit, the total revenue ($60) is less than the total cost ($28,545), so it is not the profit-maximizing quantity of output
2. For 2 units, the total revenue ($120) is less than the total cost ($28,590), so it is not the profit-maximizing quantity of output
3. For 3 units, the total revenue ($180) only just covers the total cost ($28,635), so it is the profit-maximizing quantity of output
4. For 4 units, the total revenue ($240) is more than the total cost ($28,680), so it is not the profit-maximizing quantity of output
5. For 5 units, the total revenue ($300) is more than the total cost ($28,725), so it is not the profit-maximizing quantity of output

Therefore, the profit-maximizing quantity of output is 3 units, so the correct answer is c. 475 units.