Formulating a Linear Problem

The steps for defining a linear problem include:

Identifying the decision variables.

Writing the objective function.

Mentioning the constraints.

Explicitly stating the non-negativity restriction.

A problem will be a linear problem if and only if the decision variables, objective function and constraints all are linear functions.

If all the three conditions are satisfied, then it is a linear problem.

Let Mi be the tons of coal shipped from mine i and xij be the tons of coal shipped from mine i to customer j.

LINDO is a software package for linear programming and it helps to get a good feasible solution quickly.

Hence in this case, the linear problem in LINDO form is
MIN 50 M1 + 55 M2 + 62 M3 + 4 X11 + 6 X12 + 8 X13 + 12 X14 + 9 X21 + 6 X22 + 7 X23 + 11 X24 + 8 X31 + 12 X32 + 3 X33 + 5 X34

Subject to

2) M1 <= 1203) M2 <= 100 4) M3 <= �

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Solution Summary: The author explains the steps for defining a linear problem by identifying the decision variables, writing the objective function, and stating the non-negativity restriction.

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