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 $$C ( x ) = 2 x ^ { 2 } - 32 x + 790$$ where x is the number of videos rented daily. Find the lowest cost to the nearest
Dollar.
A) $278
B) $662
C) $534
D) $918

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 lowest cost occurs at the vertex of the parabola. The x-coordinate of the vertex is given by $-b/(2a)$, where $a = 2$ and $b = -32$. Calculating this gives $x = 8$. Substituting $x = 8$ into the cost function gives the minimum cost: $C(8) = 2(8)^2 - 32(8) + 790 = 662$.

Solve the Problem C(x)=2x2−32x+790C ( x ) = 2 x ^ { 2 } - 32 x + 790C(x)=2x2−32x+790

Solve the Problem $C ( x ) = 2 x ^ { 2 } - 32 x + 790$