The document discusses how to formulate the dual of a primal linear programming problem. It provides 10 steps for converting a primal maximization problem into a dual minimization problem. As an example, it formulates the dual of the primal problem: Maximize z = -5x1 + 2x2 subject to x1 - x2 ≥ 2 and 2x1 + 3x2 ≤ 5, with non-negativity constraints. The dual is formulated as: Minimize z = -2y1 + 5y2 subject to -y1 + 2y2 ≥ -5 and y1 + 3y2 ≥ 2, with non-negativity constraints on the dual variables y1 and y2.
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2. Write the dual of the following primal problem:
Maximise: z = -5x1 + 2x2
Subject to the constraints:
x1 - x2 ≥ 2
2x1 + 3x2 ≤ 5
x1, x2 ≥ 0
3. 1. If primal is a maximisation problem, its dual will be a minimisation problem, and vice versa.
2. No. of dual variables = no. of primal constraints.
3. No. of dual constraints = no. of primal variables.
4. The transpose of the coefficient matrix of the primal is the coefficient matrix of the dual.
5. The direction of constraints of the dual is the reverse of the direction of constraints in the
primal.
6. If the kth primal constraint is a strict equality, then the kth dual variable will be unrestricted in
sign.
7. If the ith primal variable is unrestricted in sign, then the ith dual constraint will be a strict
equality.
8. If the primal is a maximisation problem, then before formulating the dual all the constraints
should be converted into ‘≤ type’. If the primal is a minimisation problem, then before
formulating the dual all the constraints should be converted into ‘≥ type’.
9. The objective function coefficients of the primal become the RHS constants of the
constraints of the dual and the RHS constants of the primal constraints become the objective
function coefficients of the variables in the dual.
10. If a variable is unrestricted in sign, it can be written as the difference between two non-
negative variables.