Consider the following LP: minz = 4x +4x+6x3 subject to x + 2x + 2x3 ...

 

Transcribed Image Text:

Consider the following LP: minz = 4x₁ +4x₂+6x3 subject to x₁ + 2x₂ + 2x3 ≥ 4 3x₁ + x2 + 12x3 ≥ 6 Xx₁ + x₂ + x3 ≤ 10 X1, X2, X30 a) Show that the basis (X2, X3, S3) is an optimal basis for the above problem and find the optimal solution. b) Write the dual of the above LP. c) Using complementary slackness, find the optimal solution of the dual problem. d) Show that strong duality holds Consider the following LP: minz = 4x₁ +4x₂+6x3 subject to x₁ + 2x₂ + 2x3 ≥ 4 3x₁ + x2 + 12x3 ≥ 6 Xx₁ + x₂ + x3 ≤ 10 X1, X2, X30 a) Show that the basis (X2, X3, S3) is an optimal basis for the above problem and find the optimal solution. b) Write the dual of the above LP. c) Using complementary slackness, find the optimal solution of the dual problem. d) Show that strong duality holds

Answer rating: 100% (QA)

To solve this linear programming problem and address the questions youve asked well follow these steps a Show that the basis x2 x3 s3 is an optimal ba... View the full answer