A company's revenue, R(x) , in thousands of dollars, from selling x thousand units is modeled by the quadratic function shown. R(x)=−x^2+9x−10 Its cost, C(x) , in thousands of dollars, is modeled by the linear function C(x)=2x How many units must the company sell to break even?
Answer
A
5 comma 000 or 10 comma 000 units
B
2 comma 000 or 5 comma 000 units
C
4 comma 000 or 10 comma 000 units
D
2 comma 000 or 4 comma 000 units
Explanation
Break-even occurs when revenue equals cost. Set −x² + 9x − 10 = 2x, which simplifies to x² − 7x + 10 = 0 after multiplying by −1. Factoring gives (x − 2)(x − 5) = 0, so x is 2 or 5 thousand units. The company must sell 2,000 or 5,000 units, choice C.
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