Calculus Optimization Question:

Question

Consider a rectangular box with a volume of 32 ft^3 that has five sides: a bottom and four vertical sides but no top. Let W be the box’s width, L be its length, and H be its height; to be realistic, we assume that W, L, and H are all positive.

Let A be the surface area of our 32 ft^3 box. Derive a formula for A in terms of only W and L (but not H).

Answer 1

32 = LWH

H = 32/LW

A = 2(LW+LH+HW)

A=2(LW+L(32/LW) + (32/LW)W)

A = 2(LW + 32/W + +32/L)