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While this could be easily done without Sage, you can have a look at Mixed Integer Linear Programming, see http://doc.sagemath.org/html/en/reference/numerical/sage/numerical/mip.html and http://doc.sagemath.org/html/en/thematic_tutorials/linear_programming.html

While this particular example could be easily done without Sage, you can have a look at Mixed Integer Linear Programming, Programming as a general method, see http://doc.sagemath.org/html/en/reference/numerical/sage/numerical/mip.html and http://doc.sagemath.org/html/en/thematic_tutorials/linear_programming.html