A Note on an Integer Programming Problem That Has a Linear Programming Solution

Abstract

It is well-known that solutions to integer programming problems usually cannot be obtained by simply solving the corresponding linear programming relaxation. There are, however, examples of integer programming problems whose solutions can be obtained by simply solving the linear program and ignoring the integer constraints. Proving that these particular models have this trait is generally beyond the scope of a beginning course in operations research. In this paper an integer programming model, with only two constraints, is presented whose solution can be directly obtained using the standard simplex method. A proof is provided that makes a connection between analysis and operations research.