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Another example

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. Answer y1=29/5 y2= -2/5. Dual Price. Z=W Z is the dollars and W should also be the dollars. W= ∑bi yi

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Another example

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  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. 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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