A box has a bottom with one edge 6 times as long as the other. If the box has no top and the volume is fixed at V, what dimensions minimize the surface area?

Answer 1

v = x(6x)*y
y = V/(6x^2)

A = x*6x + 2xy + 2*6xy = 6x^2 + 14xy
= 6x^2 + 14x(V/6x^2)
= 6x^2 + 7V/(3x)

Now just find where dA/dx = 0.