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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