SAT Math · Nonlinear functions · medium

A company's cost, in dollars, to produce x units is modeled by C(x) = 3x² - 60x + 800. How many units should be produced to minimize cost?

A company's cost, in dollars, to produce xx units is modeled by C(x)=3x2−60x+800C(x) = 3x^2 - 60x + 800. How many units should be produced to minimize cost?

Answer and explanation

Answer: D: 10

The cost function C(x)=3x2−60x+800C(x) = 3x^2 - 60x + 800 is an upward-opening parabola, so its minimum is at the vertex: x=−b2a=−−602(3)=10x = -\frac{b}{2a} = -\frac{-60}{2(3)} = 10 units, choice D. The minimum cost is C(10)=300−600+800=500C(10) = 300 - 600 + 800 = 500 dollars. Choice A (20) comes from dividing by aa instead of 2a2a. Choice B (60) is the coefficient of xx. Choice C (800) is the fixed cost, the value of C(0)C(0). The question asks how many units to produce, which is the xx-coordinate of the vertex.

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