math

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?

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  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

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