Optimization Simplex Method (Exercise)

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OptimizationSimplex Method(Exercise)
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Problem

• How many kilogram of each product to produce in
  order to maximize weekly profit?

Product 1 Product 2 Product 3 Resource Availability
Raw chemical 5 kg/kg 4 kg/kg 10 kg/kg 3000 kg
Production time 0.05 hr/kg 0.1 hr/kg 0.2 hr/kg 55 hr/week
30/kg 30/kg 35/kg
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Basic Z x1 x2 x3 S1 S2 RHS MRT
Z never


Basic Z x1 x2 x3 S1 S2 RHS MRT
Z never


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Basic Z x1 x2 x3 S1 S2 RHS MRT
Z never


Basic Z x1 x2 x3 S1 S2 RHS MRT
Z never


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Problem 2a
Basic Z x1 x2 x3 s1 s2 s3 RHS
1 0 0 -10 3 0 0 30
0 0.5 1 0 0.25 0 0 2.5
0 -0.5 0 4 -0.25 1 0 10
0 3 0 1 -0.5 0 1 30

• Which variables (besides Z) are the basic
  variables?
• What are the values of x1, x2, x3?
• Is this corner point solution optimal?

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Problem 2b
Basic Z x1 x2 x3 s1 s2 s3 RHS
1 0 0 -10 3 0 0 30
0 0.5 1 0 0.25 0 0 2.5
0 -0.5 0 4 -0.25 1 0 10
0 3 0 1 -0.5 0 1 30

• Which variable should be the entering variable
  and which variable should be the leaving
  variable?
• At the next corner point solution, what are the
  values of x1, x2, x3?