Yes, a linear programming problem can have exactly two optimal solutions. This will be the case as long as only two decision variables are used within the problem.
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The algorithms to solve an integer programming problem are either through heuristics (such as with ant colony optimization problems), branch and bound methods, or total unimodularity, which is often used in relaxing the integer bounds of the problem (however, this is usually not optimal or even feasible).
you learn linear programming before you learn the transportation problem.
Integer programming is a subset of linear programming where the feasible region is reduced to only the integer values that lie within it.
No, it will not. In fact, there is a special branch of linear programming which is called integer programming and which caters for situations where the solution must consist of integers.
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