Simplex Algorithm: An Example in 3D

Maximize 5x + 4y + 3z

subject to 2x+ 3y + z <= 5

4x + y + 2z <= 11

3x + 4y + 2z <= 8

x,y,z >=0.

Step 0: convert inequalities into equalities by introducing slack variables a,b,c.

Define: a = 5-2x-3y-z => a >=0

b = 11-4x-y-2z => b >=0

c = 8-3x-4y-2z => c >=0

F = 5x+4y + 3z, objective function

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