Question

A box with square base and rectangular sides is being designed. The material for the sides costs 20 cents per square inch and that for the too and bottom costs 10 cents per square inch. The box is to hold 150 cubic inches. What dimension of the box will minimize the cost?

Answer 1

a box with base of side x has height 150/x^2

So, the cost function is

c(x) = 10*2*x^2 + 20*4*x*150/x^2
= 20x^2 + 12000/x

so, find where dc/dx=0 for minimal cost.