CA Foundation · Quantitative Aptitude · Equations

A company's profit function is represented by P(x) = −2x² + 40x − 150, where x is the number of units produced (in hundreds). At what production level does the company break even (P = 0)?

The company breaks even at 5 hundred units or 15 hundred units. These are found by solving the quadratic equation −2x² + 40x − 150 = 0, which factors as (x − 5)(x − 15) = 0.

A5 hundred units or 15 hundred unitsCorrect
B3 hundred units or 17 hundred units
C4 hundred units or 18 hundred units
D6 hundred units or 14 hundred units

Explanation

Setting P(x) = 0: −2x² + 40x − 150 = 0. Dividing by −2: x² − 20x + 75 = 0. Using the quadratic formula or factoring: (x − 5)(x − 15) = 0, so x = 5 or x = 15. The break-even points are at 500 units and 1,500 units of production.

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A company's profit function is represented by P(x) = −2x² + 40x − 150, where x is the number of units produced (in hundreds). At what production level does the company break even (P = 0)?

Explanation

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