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Another example Max z=5x1+12x2+4x3-MR S.t. x1+2x2+x3+x4=10 2x1-x2+3x3+R=8 X1,x2,x3,x4,R >=0. The optimum table is in next slide, find the dual problem.

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Presentation on theme: "Another example Max z=5x1+12x2+4x3-MR S.t. x1+2x2+x3+x4=10 2x1-x2+3x3+R=8 X1,x2,x3,x4,R >=0. The optimum table is in next slide, find the dual problem."— Presentation transcript:

1 Another example Max z=5x1+12x2+4x3-MR S.t. x1+2x2+x3+x4=10 2x1-x2+3x3+R=8 X1,x2,x3,x4,R >=0. The optimum table is in next slide, find the dual problem and its optimal solution

2 basicx1x2x3x4Rsol z003/529/5-2/5+M54+4/5 x201-1/52/5-1/512/5 x1107/51/52/526/5 Answer y1=29/5 y2= -2/5

3 Dual Price Z=W Z is the dollars and W should also be the dollars. W= bi yi bi represents the number of units available of resource i. Therefore Dollars= unit of resource i X yi Hence yi= dollars/unit of resource I So yi or dual price or shadow price of a resource I is the worth per unit of resource i.

4 Dual Price Each dual price is associated with a constraint. It is the amount of improvement in the objective function value that is caused by a one-unit increase in the RHS of the constraint. It is also called Shadow Price.

5 More on Dual Price: A dual price can be negative, which shows a negative ( or worse off) contribution to the objective function value by an additional unit of RHS increase of the constraint.

6 Primal and Dual in LP Each linear program has another associated with it. They are called a pair of primal and dual. Primal and dual have equal optimal objective function values. The solution of the dual is the dual prices of the primal, and vice versa.


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