Chapter 12.4, Problem 41E

a.

To determine

To find: A model for the average cost per unit produced.

Answer to Problem 41E

  $\text{Average cost per unit}$

  $\overline{C}=73+\frac{25000}{x}.$

Explanation of Solution

Given information: The cost function for a certain model of MP3 player is

  $C=73x+25,000,$ where C is in dollars and x is the number of MP3 players produced.

Calculation:

To find average cost/unit.

Average cost per unit= $\frac{Total\cos t}{no.ofunits}$ .

  $\begin{array}{l}\text{Average cost per unit}=\frac{73x+25000}{x}.\\ \overline{C}=73+\frac{25000}{x}.\end{array}$

b.

To determine

To find: The average costs per unit when $x=1000,x=5000\text{and}x=10,000.$

Answer to Problem 41E

  $\begin{array}{l}x=1000,\overline{C}=98\$.\\ x=5000,\overline{C}=78\$.\\ x=10,000,\overline{C}=75.5\$.\end{array}$

Explanation of Solution

Given information: The cost function for a certain model of MP3 player is

  $C=73x+25,000,$ where C is in dollars and x is the number of MP3 players produced.

Calculation:

  $\text{Average cost per unit}$

  $\begin{array}{l}\overline{C}=73+\frac{25000}{x}.\\ x=1000.\\ \overline{C}=73+\frac{25000}{1000}=98\$\\ x=5000.\\ \overline{C}=73+\frac{25000}{5000}=78\$\\ x=10,000.\\ \overline{C}=73+\frac{25000}{10000}=75.5\$\end{array}$