Sensitivity_Problem session

# Sensitivity_Problem session - MS&E 211 The Simplex Tableau...

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The Simplex Tableau in Production Form Initial Tableau: x slack RHS Basis - c 0 0 A I b Final Tableau: Basis - c +y*A y* c B B -1 b B -1 A B -1 B -1 b Where y*= c B B -1 , the dual solution to the production problem

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Sample Problem: The Concrete Products Corporation has the capability of producing four types of concrete blocks. Each block must be subjected to three processes: batch mixing, mold vibrating and inspection. The plant manager desires to maximize the profit during the next month. During the upcoming thirty days, he has 800 machine hours available on the batch mixer, 1000 hours on the mold vibrator and 340 man-hours of inspection time. The problem is formulated as follows: max 8x1 + 14x2 + 30x3 + 50x4 S.t. x1 + 2 x2 + 10x3 + 16x4 <= 800 1.5x1 + 2 x2 + 4 x3 + 5 x4 <= 1000 0.5x1 + 0.6x2 + x3 + 2 x4 <= 340 where xi is the production level of the ith product; i = 1, 2, 3, 4.
The Final Tableau: Basic x1 x2 x3 x4 x5 x6 x7 RHS B 0 0 28 40 5 2 0 6000 2 0 1 11 19 1.5 -1 0 200 1 1 0 -12 -22 -2 2 0 400 7 0 0 -4 1.6 .1 -.4 1 20 B -1 - c +y*A y* B -1 b

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## This note was uploaded on 06/16/2010 for the course MS&E 211 taught by Professor Yinyuye during the Fall '07 term at Stanford.

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Sensitivity_Problem session - MS&E 211 The Simplex Tableau...

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