How Can I Optimize Dimensions for Garden Boxes with Minimal Material?

[dcheney214]

Im trying to build garden boxes this summer and I am trying to determine the dimensions through optimization. Its been a long time since I've done this and I can't seem to model this mathematically.

Id like a box where the volume=13.5ft^3 and the height of the frame to be 8 inches or .66ft. Id like to minimize the amount of material used.
I guess I am more bothered that this is a fairly simple problem and I can't remember how to model it. I am more concerned with the method than the answer.

Thanks.

 

[Stephen Tashi]

Id like to minimize the amount of material used.
I guess I am more bothered that this is a fairly simple problem and I can't remember how to model it.

It isn't a simple problem in the real world. For example, materials such as lumber are usually available only in standard lengths. If you need a 5 ft board from 8 ft lumber and don't use the 3 ft "scrap" left over then you must account for what is wasted in your tally of "amount of material".

If you ignore such real world aspects you can begin by writing the expression for the total amount of material in terms of variables representing the (as yet unknown) dimensions of the box. Do that and someone can help you proceed. (For example, we don't know if your box has a bottom or whether it is just a "frame".)