The US Post Office has a limit on the size of packages it will accept for mailing. The length plus the girth must be 84 inches or less. Find the dimensions of the rectangular package with a square end, which will maximize the volume of the package.

Answer 1

4x +y = 84
so
y = (84-4x)

Volume = x^2 y = x^2(84-4x)

V = 84 x^2 - 4 x^3
dV/dx = 0 for max or min
0 = 168 x - 12 x^2
0 = x (168-12 x)
x = 0 not very useful so
x = 168/12 = 14
y = length = 28
interesting, length twice the side dimension

Answer 2

Wait don't you plus x=14 back in to y=(84-4x)? Cause y then equals 20 in

Answer 3

well on my calculator 84 -14*4) = 28