I am having trouble setting up the following problem.
A rectangular storage container with an open top is to have a volume of 10 m3. The length of this base is twice the width. Material for the base costs $10 per square meter. Material for the sides costs $6 per square meter. Find the cost of materials for the cheapest such container.
I really don't see what equations I could get out of that information.
While I am at it, I have never worked with optimization problems that involve radians.
A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one-third of the sheet on each side through an angle θ. How should θ be chosen so that the gutter will carry the maximum amount of water?
Again I just need someone to point me in the right direction. Namely, how and what the equations should be.