# Calc 1: Urgent, Optimize

• Dec 6th 2006, 10:48 AM
Bloden
Calc 1: Urgent, Optimize
A shipping company limits the size of a mailable parcel. The longest side plus the girth (the perimeter of a cross section perpendicular to the longest side) may not exceed 108 inches" 1.) Which mailable cube has the largest volume? 2.) Find the dimensions of the mailable rectangular parcel with a square base that has the largest volume. 3.) Among mailable right circular cylinders, which has the largest volume?

This is due in 10-15 mins if someone by chance reads this in time. Thanks
• Dec 6th 2006, 10:19 PM
CaptainBlack
Quote:

Originally Posted by Bloden
A shipping company limits the size of a mailable parcel. The longest side plus the girth (the perimeter of a cross section perpendicular to the longest side) may not exceed 108 inches" 1.) Which mailable cube has the largest volume? 2.) Find the dimensions of the mailable rectangular parcel with a square base that has the largest volume. 3.) Among mailable right circular cylinders, which has the largest volume?

This is due in 10-15 mins if someone by chance reads this in time. Thanks

1) For a cube the girth plus the longest side is 5s, where s is the length of the side.
So for the largest cube:

5s=108,

or

s=21.6 inches

2) Let the side of the square base be s and the length be l, then:

4s+l=108,

The volume is:

V=s^2 x l=s^2 (108-4s)

The largest volume corresponds to one of the solutions of dV/ds=0, so:

216 s -12s^2=0,

one root is s=0, which is not the one we want, the other is s=216/12=18 inches,
from which we get l=36 inches.

3) solution method is similar to 2)

RonL