A teck company has fixed monthly costs of $10,000 and variable costs of $50 per service provided. The expense function based on the selling price p of the service is E(p)=−50p+10,000 The revenue function in terms of the selling price p is R(p)=−5p^2+500p When does the company make a profit?
Answer
A
When the price is more than 10 dollars but less than 100 dollars per service
B
When the price is more than 0 dollars but less than 100 dollars per service
C
When the price is less than 22 point 9 9 dollars or more than 87 point 0 2 dollars per service
D
When the price is more than 22 point 9 9 dollars but less than 87 point 0 2 dollars per service
Explanation
Profit is revenue minus expense: P(p) = R(p) − E(p) = −5p² + 550p − 10,000. Setting profit equal to zero gives −5p² + 550p − 10,000 = 0, whose break-even prices are about $22.99 and $87.02. Since the profit quadratic opens downward, profit is positive between those prices, so the company makes a profit when the price is more than $22.99 but less than $87.02 per service.
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