A factory's daily production cost, in dollars, for producing x units is modeled by C(x) = 2x² - 40x + 500. How many units should be…

The cost function $C(x) = 2x^2 - 40x + 500$ is an upward-opening parabola, so its minimum is at the vertex: $x = -\frac{b}{2a} = -\frac{-40}{2(2)} = 10$ units, choice D. The minimum cost is $C(10) = 200 - 400 + 500 = 300$ dollars. Choice A (20) comes from using $-\frac{b}{a}$, forgetting to double the denominator. Choice B (40) is the coefficient of $x$. Choice C (500) is the fixed cost, $C(0)$. The question asks for the number of units, which is the vertex's $x$-coordinate, not the cost.