Question

How do you express the cost of making x small boxes, y medium boxes, and z large boxes, it costs $2.50 to make a small box, $4.00 for a medium box, and $4.50 for a large box and the fixed costs are $8000?

Answer 1

This problem has of course a multiplicative nature. I simply mean that if you produce twice the boxes, you will pay twice the price.

So, how much will it cost to produce `x` small boxes? Each small box costs `$2.50`, so the total will be `$2.50 \cdot x`

For the same reason, the price to pay to produce `y` medium boxes will be `$4.00 \cdot y`, and the price to produce `z` large boxes will be `$4.50 \cdot z`.

If all of the three prices must be fixes at `$8000`, your problem is expressed with mathematical notation by writing that
`$2.50 \cdot x=8000`,
`$4.00 \cdot y=8000`, and
`$4.50 \cdot z=8000`,

where `x`, `y` and `z` are, as you said, the number of small, medium and large boxes.