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Please answer the question with details (Step-by-Step): An oil filter manufacturing company has a capacity of...

Please answer the question with details (Step-by-Step):

An oil filter manufacturing company has a capacity of 500,000 units annually. The fixed cost of the production line is $400,000 per year with a variable cost of $6 per unit and revenues of $9 per unit. The percentage of capacity that must be utilized for the company to breakdown is closest to:

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Answer #1

Let the breakeven units be X, then

Total cost = Fixed cost + variable cost

Total cost = 400000 + 6*X

Total revenue = Price * Quantity

= 9*X

For breakeven

Total cost = Total revenue

400000 + 6*X = 9*X

3*X = 400000

X = 133333.33

Capicity utilization = 133333.33 / 500000 * 100 = 26.67%

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