Web Reference: Dec 17, 2025 · Step 1: Formulate the linear programming problems based on the given constraints. Step 2: Convert all the given inequalities to equations or equalities of the linear programming problems by adding the slack variable to each inequality where ever required. Graphical solution is limited to linear programming models containing only two decision variables (can be used with three variables but only with great difficulty). These inequalities can be replaced by equalities since the total supply is equal to the total demand. A linear programming formulation of this transportation problem is therefore given by: Minimize 5x11 + 5x12 + 3x13 + 6x21 + 4x22 + x23 subject to: x11 + x21 = 8 x12 + x22 = 5 x13 + x23 = 2 x11 + x12 + x13 = 6 x21 + x22 + x23 = 9 x11 0; x21 x31 ...
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