The postal service places a limit of 84 inches on the combined lenght and girth (distance around) of a package to be sen parcel post. What Dimensions of a rectangular box with square cross-section will contain the largest volume that can be mailed?

Answer 1

4x+y = 84, so
y = 84-4x

v = x^2 y = x^2(84-4x) = 84x^2 - 4x^3
dv/dx = 168x - 12x^2
= 12x(14-x)

dv/dx=0 when x=14

so the box is 14 x 14 x 28