Question

The average cost when producing x items is found by dividing the cost function, C(x), by the number of items, x. When is the average cost less than 100, given the cost function is C(x) = 10x + 180?

Answer 1

The average cost is less than 100 when the number of items x is greater than 2

Explanation:

The cost equation is
`C(x) = 10x + 180`

The average cost
`Cp = (C(x))/(x)`

We want to know when the cost Cp is less than 100.

So

`Cp <100`

`Cp = (C(x))/(x) <100`

`10 + (180)/(x) <100\\\\(180)/(x) <90`

For
`x> 0`

`(180)/(90) <x`

`x> 2`

The average cost is less than 100 when
`x>2`