The Simplex Method Standard Form. Furniture Manufacturing Problem 63100096 11010018 26001072 -80-7000010 x y u v w M Carp. Finish. Uph.

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Presentation transcript:

The Simplex Method Standard Form

Furniture Manufacturing Problem x y u v w M Carp. Finish. Uph.

Selecting the Pivot Column: x y u v w M Carp. Finish. Uph. Objective Function: 80x + 70y = M Which would we want to make first chairs or sofas?

Selecting the Pivot Column: x y u v w M Carp. Finish. Uph. PIVOT COLUMN Largest Negative in the bottom row

Selecting the Pivot Row: x y u v w M Carp. Finish. Uph. First a bit of Trial and Error…

x y u v w M CFUCFU CFUCFU CFUCFU ½ 1/ ½ -1/ / / CFUCFU CFUCFU CFUCFU ½-½ ½ x y u v w M

1½ 1/ ½ -1/ / / CFUCFU CFUCFU CFUCFU ½-½ ½ x y u v w M x = 16 y = 0 u = 0 v = 2 w = 40 M = 1280 x = 18 y = 0 u = -12 v = 0 w = 36 M = 1440 x = 36 y = 0 u = -120 v = -18 w = 0 M = 2880

Selecting the Pivot Row: /6 = /1 = /2 = x y u v w M RATIOS Carp. Finish. Uph.

Selecting the Pivot Row: /6 = /1 = /2 = x y u v w M RATIOS Carp. Finish. Uph. PIVOT ROW Smallest Non-Negative Ratio

Putting it all together: x y u v w M Carp. Finish. Uph.

After Completing the Pivot: Are We Done Yet??? 1½1/ ½-1/ / / x y u v w M Carp. Finish. Uph.

Pivot Column: 1½1/ ½-1/ / / x y u v w M Carp. Finish. Uph. PIVOT COLUMN Largest Negative in the bottom row

Pivot Row: 1½1/ /(1/2) = 32 0½-1/610022/(1/2) = / /5 = / x y u v w M Carp. Finish. Uph. PIVOT ROW Smallest Non-Negative Ratio

After Completing the Pivot: Are We Done Yet??? 101/ / / / x y u v w M Carp. Finish. Uph.

FINAL ANSWER: 101/ / / / x y u v w M Carp. Finish. Uph. 14 chairs, 4 sofas Profit of $1400

Maximize 10x + 12y + 10z subject to:

x - 2y + u = 6 3x + z +v = 9 y + 3z +w = x - 12y - 10z +M = 0 System of Equations:

Simplex Tableau: x y z u v w M

Simplex Tableau: /(-2) = /(0) undefined /(1) = x y z u v w M Ratios PIVOT COLUMN PIVOT ROW

New Simplex Tableau: x y z u v w M x = 0, y = 12, z = 0 M = 144

New Simplex Tableau: /1 = /3 = / x y z u v w M PIVOT COLUMN PIVOT ROW

New Simplex Tableau: 0017/31- 1/ / /3010/ x y z u v w M x = 3, y = 12, z = 0 M = 174