A rectangular storage container with an open top is to have a volume of k cubic meters. The length of its base is twice its width. The material for the base costs $6 per square meters and the material for the sides costs $10 per square meter.

Answer 1

y=2x
xyz=k, so z=k/2x^2

the cost c is

c(x,y,z) = 6xy + 10(2xz + 2yz)
c(x) = 6x(2x) + 20(3x)(k/2x^2)
= 12x^2 + 30k/x