Question
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?
Answers
Steve
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
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