Question

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)=7.6x + 10,800 a 200 items b. 2000 items c. 5000 items a. What is the average cost per item when 200 items are produced?

Answer 1

Given :Cost function :
`C(x)=7.6x + 10,800`

To Find : Find the average cost per item when the required number of items is produced

Solution:

a) 200 items

Cost function :
`C(x)=7.6x + 10,800`

Substitute x = 200

`C(200)=7.6(200)+ 10,800`

`C(200)=12320`

So, Total cost of producing 200 items is 12320

Now Average cost per item =
`\frac{\text{Total cost}}{\text{No. of items}}`

Average cost per item=
`(12320)/(200)`

Average cost per item=61.6

So, the average cost per item when 200 items are produced is 61.6 .

b) 2000 items

Cost function :
`C(x)=7.6x + 10,800`

Substitute x = 2000

`C(2000)=7.6(2000)+ 10,800`

`C(2000)=26000`

So, Total cost of producing 2000 items is 26000

Now Average cost per item =
`\frac{\text{Total cost}}{\text{No. of items}}`

Average cost per item=
`(26000)/(2000)`

Average cost per item=13

So, the average cost per item when 2000 items are produced is 13.

c) 5000 items

Cost function :
`C(x)=7.6x + 10,800`

Substitute x = 5000

`C(5000)=7.6(5000)+ 10,800`

`C(5000)=48800`

So, Total cost of producing 5000 items is 48800

Now Average cost per item =
`\frac{\text{Total cost}}{\text{No. of items}}`

Average cost per item=
`(48800)/(5000)`

Average cost per item=9.76

So, the average cost per item when 5000 items are produced is 9.76