Thread: Maximize volume, minimize surface area (3 dimensions)

I was assigned this single problem as part of a group project my instructor gave us. He says outright that these problems are much harder than what we were already tested on (group projects are due after the test) and we will need to seek extra help outside of class as a way to expand on current knowledge. Could anybody point me in the right direction, or maybe get the problem set-up for me to compute?

"2. A trash bin with no lid has five sides and is in the shape of a trapezoidal prism as shown in the figure below. If the volume of the bin is to be 16.0 m^3, determine the values of a,b, and c which minimize the surface area."




Thanks so much for any help!

Dylan

This is a problem for the method of Lagrange multipliers.

--Kevin C.