In the cost function below, C(x) is the cost of producing x items. Find the average cost per item when the required number of items is produced. C(x) = 4.1% +9,500 a. 200 items b. 2000 itemsC. 5000 items What is the average cost per item when 200, 2000, and 5000 items ?

Respuesta :

Since the function of the cost is

[tex]C(x)=4.1x+9500[/tex]

Where x is the number of the items

a) There were 200 items

x = 200

[tex]\begin{gathered} C(x)=4.1(200)+9500 \\ C(x)=820+9500 \\ C(x)=10320 \end{gathered}[/tex]

To find the average cost per item, find

[tex]\begin{gathered} \text{Ave. =}\frac{C(x)}{x} \\ \text{Ave. = }\frac{10320}{200} \\ \text{Ave. =51.6} \end{gathered}[/tex]

b) There were 2000 items

[tex]x=2000[/tex]

[tex]\begin{gathered} C(2000)=4.1\times2000+9500 \\ C(2000)=17700 \end{gathered}[/tex]

Find the average as the same above

[tex]\begin{gathered} \text{Ave. = }\frac{17700}{2000} \\ \text{Ave. = 8.85} \end{gathered}[/tex]

c) There were 5000 items

[tex]x=5000[/tex][tex]\begin{gathered} C(5000)=4.1(5000)+9500 \\ C(5000)=30000 \end{gathered}[/tex]

Divide it by 5000 to find the average

[tex]\begin{gathered} \text{Ave. = }\frac{30000}{5000} \\ \text{Ave. = 6} \end{gathered}[/tex]