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.

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windyyork windyyork · Answer 1 · 2019-10-30T06:47:09+01:00

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

Step-by-step 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 = [tex]5\times 5\times 5=125\ cm^3[/tex]

Volume of cuboidal box = [tex]2\times 4\times 5=40\ cm^3[/tex]

Volume of foam packing in a standard box is given by

[tex]125-40=85\ cm^3[/tex]

Total cost of widget packed in a standard box would be

[tex]85\times 0.03+0.80\\\\=\$3.35[/tex]

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

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