Solve the problem.
-The owner of a video store has determined that the cost C, in dollars, of operating the store is approximately given by $$C ( x ) = 2 x ^ { 2 } - 32 x + 530$$ , where x is the number of videos rented daily. Find the lowest cost to the nearest
Dollar.
A) $658
B) $274
C) $402
D) $18

Question

Quizplus · Accepted Answer

The cost function C(x) is a quadratic function, which opens upwards (since the coefficient of $x^2$ is positive). The vertex of this parabola gives the minimum cost. The x-coordinate of the vertex is given by $-b/(2a)$. Here, $a = 2$ and $b = -32$, so $x = 8$. Plugging $x = 8$ back into the cost function gives the minimum cost: $C(8) = 2(8)^2 - 32(8) + 530 = 402$.

Solve the Problem C(x)=2x2−32x+530C ( x ) = 2 x ^ { 2 } - 32 x + 530C(x)=2x2−32x+530

Solve the Problem $C ( x ) = 2 x ^ { 2 } - 32 x + 530$