Question

A manufacturer needs to pay $300 to start making a certain new product. Besides the initial costs of $300, this product will also cost $18 per unit. The manufacturer wants to write an inequality to determine when the average cost per unit will be $24 or less.

Which inequality determines how many units (x) of the product need to be produced for the average cost to be $24 or less?

Answer 1

`\displaystyle (300+18x)/(x)\le 24`

Explanation:

Average Cost

Making a certain new product costs $300 plus $18 per product.

The total cost for x products is given by:

300 + 18x

To get the average cost, we divide the total cost by the number of products manufactured:

`\displaystyle A=(300+18x)/(x)`

If the manufacturer wants to keep the average cost at $24 or less:

`\mathbf{\displaystyle (300+18x)/(x)\le 24}`

This is the required inequality