Minimize the cost of building a box given a volume constraint and using 4"x8' wood boards

[husserl555]

Hi,
I've been having some trouble figuring this out. Say I want to build a compost box (4 sides and a lid) out of 4"x8' wood boards at $2.50 per board and I want the box to be able to contain at least 30 sq ft of compost. How can I calculate the dimensions that will achieve my volume constraint but minimize my costs (i.e the amount of wood that will be lost due to cuts)?

Any help is much appreciated

 

[Otis]

… contain at least 30 sq ft of compost … [and] minimize … [loss] due to cuts …

Hi husserl. I think you meant to say at least 30 cubic feet of compost. Do you have an upper limit on the height? Adding height could potentially make use of leftover pieces (i.e., not require additional boards). Also, what's the minimum depth, for composting? For example, you could build a box (and lid) with 21 complete boards, but the box would be only one foot high. Height thresholds not withstanding, I've assumed you don't care what the footprint is.

?