duality-transformation

duality-transformation - Here is the original problem from...

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Here is the original problem from McCarl and Spreen Max 3x1 – 2x2 + X3 St x1 + x2 + 2x3 = 20 -2x1 +x2 + x3 ge 10 X1 less than or equal to zero. X2 non-negative and X3 unrestricted. x1 x2 x3 Used SP obj 3 -2 1 10 c1 1 1 2 eq 20 20 0.5 c2 -2 1 1 ge 10 10 0 answer 0 0 10 rc 2.5 -2.5 0 The original primal problem, set up and solved in Excel with appropriate restrictions on signs of X1 and X2. (X3 unrestricted). You should be able to pop this open and see the constraints. This dual can be taken directly, using our "rules for duals." Min 20y1 +10 y2 s.t. y1 - 2y2 le 3 y1 + y2 ge -2 2y1 + y2 = 1 Y1 is unrestricted, y2 le 0. Here is the solution of the direct dual. Note that the SP of the dual is equal to the solution to the primal and vice versa. Also notice that the reduced costs in the primal equal the surplus/slack in the dual. (The reduced costs in the dual are 0 because both constraints in the primal are exactly satisfied)
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Y1 Y2 used SP min 20 10 10 1 -2 le 3 0.5 0 1 1 ge -2 0.5 0 2 1 eq 1 1 10 answers 0.5
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duality-transformation - Here is the original problem from...

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