Express the cost of materials as a function of the width of the base.

Question

A rectangular storage container with an open top has a volume of 20 m3 . The length of its base is twice its width. Material for the base costs $10 per square meter; material for the sides costs $5 per square meter. Express the cost of materials as a function of the width of the base.

Answer 1

Let x = the width and y = the height of the container.

Volume V=2x²y=20

y=10/x²

Cost, C = 10(2x²) + 5(2•2xy + 2xy)

=20x²+30xy

=20x²+30x(10/x²)

C(x) = 20x²+300/x