Question

A rectangular storage container with an open top is to have a volume of 18 cubic meters. The length of its base is twice the width. Material for the base costs 13 dollars per square meter. Material for the sides costs 7 dollars per square meter. Find the cost of materials for the cheapest such container.

Answer 1

volume=lwh=18
area of base=lw=2w^2
area of side=2lh+2wh=2wh+4wh=6wh

Answer 2

so cost of base=13*2w^2=26w^2
cost of sides=7*6wh=54wh

h=18/lw=18/2w^2=9/w^2

thus, the total cost=26w^2+52w(9/w^2)=26w^2+468/w

differentiate that and set it to zero

Answer 3

I got -2^(1/3) 3^(2/3) when i set it =0