A jewelry box with a square base is to be built with copper plated sides, nickel plated bottom and top and a volume of 40cm^3. if nickel plating costs $2 per cm^2 and copper plating costs $1 per cm^2, find the dimensions of the box to maximize the cost of the materials?

Answer 1

not sure why you'd want to maximize the costs, but the initial steps are the same.

Box has sides of x, and height y. We know that

x^2y = 40, so y = 40/x^2

So, the cost is

c(x) = 2*2*x^2 + 1*4*xy = 4x^2 + 160/x

I think you can see that there is no maximum value, so now just find the minimum, where dc/dx = 0