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+15x−28 Its cost, C(x) , in thousands of dollars, is modeled by the linear function C(x)=4x How many units must the company sell to break even?
Answer
A
16 comma 000 or 28 comma 000 units
B
4 comma 000 or 7 comma 000 units
C
7 comma 000 or 28 comma 000 units
D
4 comma 000 or 16 comma 000 units
Explanation
Break-even occurs when revenue equals cost, so set −x² + 15x − 28 = 4x. Rearranging gives x² − 11x + 28 = 0, which factors as (x − 4)(x − 7) = 0. Thus x = 4 or 7, and since x measures thousands of units, the company must sell 4,000 or 7,000 units.
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