Question

A rectangular storage container with an open top is to have a volume of 10 . The length of its base is twice the width. Material for the base costs $12 per square meter. Material for the sides costs $5 per square meter. Find the cost of materials for the cheapest such container.

Answer 1

If the base has dimensions x and 2x, then we have

2x^2y = 10
so, y = 5/x^2

So, the cost of the container is

c(x) = 12*2x^2 + 5*2xy + 5*xy = 24x^2 + 15xy = 24x^2 + 75/x

so, find c(x) when dc/dx=0

Answer 2

Would dc/dx=0 when x is 1.16?

Answer 3

yes