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+12x−18 Its cost, C(x) , in thousands of dollars, is modeled by the linear function C(x)=3x How many units must the company sell to break even?
Answer
A
0 or 6 comma 000 units
B
9 comma 000 or 18 comma 000 units
C
3 comma 000 or 9 comma 000 units
D
3 comma 000 or 6 comma 000 units
Explanation
Break-even occurs when revenue equals cost. Set −x² + 12x − 18 = 3x, which simplifies to x² − 9x + 18 = 0; factoring gives (x − 3)(x − 6) = 0. Since x is measured in thousands of units, the company must sell 3,000 or 6,000 units, matching choice B.
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