Question

A toolshed with a square base and a flat roof is to have a volume of 800 cubic feet. If the floor costs $6 per square foot, the roof $2 per square foot, and the sides $5 per square foot, determine the dimensions of the least expensive shed.

Answer 1

x^2y = 800
y = 800/x^2

c = 6*x^2 + 2*x^2 + 5*4*xy
= 8x^2 + 1600/x
dc/dx = 16x - 1600/x^2 = 16(x^3-100)/x^2
dc/dx=0 at x=∛100

so, the shed is ∛100 x ∛100 x 8∛100