Solve the problem.
-The owner of a video store has determined that the cost $\mathrm { C }$, 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 $C(x) = 2x^2 - 32x + 530$ is a quadratic function that opens upwards (since the coefficient of $x^2$ is positive). The vertex of this parabola represents the minimum point. The x-coordinate of the vertex is given by $-b/(2a)$, where $a = 2$ and $b = -32$. Calculating this gives $x = 8$. Substituting $x = 8$ back into the cost function gives the minimum cost: $C(8) = 2(8)^2 - 32(8) + 530 = 402$. Thus, the lowest cost is $\$402$.

Solve the Problem C\mathrm { C }C , in Dollars, of Operating the Store Is Approximately Given

Solve the Problem $\mathrm { C }$ , in Dollars, of Operating the Store Is Approximately Given