Question

A manufacturing company needs boxes to ship their newest widget, which measures 2×4×5 in^3. Standard size boxes, 5-inch cubes, are inexpensive but require foam packaging so the widget is not damaged in transit. Foam packaging costs $0.03 per cubic inch. Specially designed boxes are more expensive but do not require foam packing. If the standard size box costs $0.80 each, and the specially designed box costs $3.00 each, which kind of box should the company choose? Explain your answer.

Answer 1

Answer: Specially designed box should be chosen by the company.

Explanation:

Since we have given that

Length of standard size cube box = 5 inches

Length of boxes needs to ship their widget = 2 inches

Width of boxes needs to ship their widget = 4 inches

Height of boxes needs to ship their widget = 5 inches

So, Volume of cubic box =
`5* 5* 5=125\ cm^3`

Volume of cuboidal box =
`2* 4* 5=40\ cm^3`

Volume of foam packing in a standard box is given by

`125-40=85\ cm^3`

Total cost of widget packed in a standard box would be

`85* 0.03+0.80\\\\=\$3.35`

So, the specially designed box which costs $3.00 is the most cost effective.

Hence, Specially designed box should be chosen by the company.