This is optimization problem I want to set up equations or s

This is optimization problem.

I want to set up equations (or system) to solve if we want to fill the big rectangular prism with the small rectangular prism. And, you need to think about the value of the small rectangular prisms. How to set the equations?

Properties:

Big Rectangular prism: Height Width Length

Small Rectangular prism: height width length value

I set x1, x2, x3, ... xn to present quantity of the small rectangular prism or just present as variables of each type of the prism.

I know the z value for the optimization is z=value1*x1+value2*x2+value3*x3+ ... + valuen*xn.

But, furthermore, what characteristics (volume, area, etc) can be used to solve this problem? And, what would be the final system for it?

Solution

Condition need to be applied only on volume because we have rectangular prisms. so if volumns are v1, v2....vn then we have sum of all volumns = volumn of the bigger prism.

But number of prisms are to be integers so it is an integer programming problem so general simplex method will not work.