The post office will accept packages whose combined length and girth is at most 42 inches. (the girth is the perimeter/distance around the package perpendicular to the length; for a rectangular box, the length is the largest of the three dimensions.) what is the largest volume that can be sent in a rectangular box? (round answer to 2 decimal places.)

Question

Mathematics

Immanuel Rodgers

10 April, 03:40

The post office will accept packages whose combined length and girth is at most 42 inches. (the girth is the perimeter/distance around the package perpendicular to the length; for a rectangular box, the length is the largest of the three dimensions.) what is the largest volume that can be sent in a rectangular box? (round answer to 2 decimal places.)

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Karissa Yates · Answer 1

If x represents the length of the box, then 42-x will be the girth. Since the largest area for a given girth is that of a square, the side length of the square cross section is (42 - x) / 4.

The volume as a function of package length is then

... v (x) = x ((42-x) / 4) ^2

This has a maximum at x=14. The corresponding volume is 686 in^3.