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