Optimization Minimize Weight

Your iron works has contracted to design and build a 500-cubic foot, square based, open topped, rectangular steel holding tank for a paper company. The tank is to be made by welding thin stainless steel plates together along their edges. As the production engineer, your job is to find dimensions for the base and height that will make the tank weigh as little as possible. What dimensions do you tell the shop to use?

© SolutionLibrary Inc. solutionlibary.com 9836dcf9d7 https://solutionlibrary.com/math/linear-transformation/optimization-minimize-weight-2v8

Solution Preview

...x^2+4xy. We want to minimized the surface so that the tank weigh as little as possible.
We know the volume of the tank is x*x*y=500. ...