Duality in linear programming
Corresponding to every linear programming problem, there is another linear programming problem. The given problem is called the primal and the other its dual. Although the idea of duality is essentially mathematical, it has important interpretations. This can help managers in answering questions about alternative courses of action and their effect on values of the objective function. When the primal problem is of the maximisation type the dual is of the minimisation type and vice versa. It is an interesting feature of the simplex method that we can use it to solve either the original problem – the primal – or the dual. Whichever problem we start out to solve, it will also give us the solution to the other problem. Consider the following general linear programming problem. Maximise Z = c1x1 + c2x2, Subject to a11x1 + a12x2 <or = b1 a21x1 + b22x2 <or = b2 x1,x2 > Continue reading