Chapter 4.1, Problem 32PPS

(a)

To determine

To Find: The number of the frames that is used to minimizes the cost.

Answer to Problem 32PPS

The number of frames that minimizes the cost is 800.

Explanation of Solution

Given:

The expression for the cost of the frames is $C=0.000025f^2-0.04f+40$ .

The f is the number of frames produced.

Calculation:

Consider the x coordinate of the vertex is,

  $x=\frac{-b}{2a}$

Then,

  $\begin{array}{c}x=\frac{-\left(-0.04\right)}{2\left(0.000025\right)}\end{array}$

   $\begin{array}{c}=800\end{array}$

Thus, the number of frames that minimizes the cost is 800.

(b)

To determine

To Find: The total cost for the number of frames.

Answer to Problem 32PPS

The total cost for the frame is $ $24$ .

Explanation of Solution

Consider the given function is,

  $C=0.000025f^2-0.04f+40$

Then,

  $\begin{array}{c}C=0.000025{\left(800\right)}^2-0.04\left(800\right)+40\end{array}$

    $\begin{array}{c}=24\end{array}$