A parcel delivery service will deliver a package only if the length plus the girth (distance around, taken perpendicular to the length) does not exceed 100 inches. Find the maximum volume of a rectangular box with square ends that satisfies the delivery company's requirements.

Question

anonymous · Answer

L +2W+2D =< 100

for a rectangle with square ends  D=W
L+4W =<100

V= LW^2
use L=100 -4W to sub.s in
V= (100-4W)W^2

Vmax is at:  V' = 0 =  200W -12W^2

solve for W
use W to find L
use L and W to find Vmax.