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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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.
It is a solution.
regardless of what the problem is, they are always called integers. unless you have variables or fractions in the problem.
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.