The following LP describes a company that makes 2 products, with 3 constraints. The optimal tableau...

 

Transcribed Image Text:

The following LP describes a company that makes 2 products, with 3 constraints. The optimal tableau is given below. (The big M method was used to solve the problem, s3 is the slack of the third constraint, e₂ is the excess variable of the second constraint, and a₁, a2 are the artificial variables of the first and second constraints.) Answer each part using sensitivity analysis. Do not solve from scratch! Show your work. Each part is independent of the others. 2 1 0 0 0 max 21 T₂ 0 0 1 0 GC 2=421 +2₂ 21 +222=6 11-1₂ 23 221 +2₂ ≤ 10 21, 22 20 €2 33 01 02 RHS 0 7/3 M-2/3 M 58/3 0-1/3 2/3 0 2/3 -1/3] 0 14/3 -1 -1 0 1 0 0 2/3 0 1 1 (a) What is the dual of this LP? (b). What is the most that the company should be willing to pay for an extra unit of resource 37 (c). Find the range of values for by (the RHS of the third constraint, which is 10 now) for which the current basis remains optimal. (d). A new constraint is added: ₁ +2 < 5. Clearly the old optimal solution is not feasible to this new constraint. Using sensitivity analysis and dual Simplex, add this new constraint to the tableau and find the new optimal tableau. (Do not solve from scratch!) 28 The following LP describes a company that makes 2 products, with 3 constraints. The optimal tableau is given below. (The big M method was used to solve the problem, s3 is the slack of the third constraint, e₂ is the excess variable of the second constraint, and a₁, a2 are the artificial variables of the first and second constraints.) Answer each part using sensitivity analysis. Do not solve from scratch! Show your work. Each part is independent of the others. 2 1 0 0 0 max 21 T₂ 0 0 1 0 GC 2=421 +2₂ 21 +222=6 11-1₂ 23 221 +2₂ ≤ 10 21, 22 20 €2 33 01 02 RHS 0 7/3 M-2/3 M 58/3 0-1/3 2/3 0 2/3 -1/3] 0 14/3 -1 -1 0 1 0 0 2/3 0 1 1 (a) What is the dual of this LP? (b). What is the most that the company should be willing to pay for an extra unit of resource 37 (c). Find the range of values for by (the RHS of the third constraint, which is 10 now) for which the current basis remains optimal. (d). A new constraint is added: ₁ +2 < 5. Clearly the old optimal solution is not feasible to this new constraint. Using sensitivity analysis and dual Simplex, add this new constraint to the tableau and find the new optimal tableau. (Do not solve from scratch!) 28

Answer rating: 100% (QA)

Step 11 The ideal IP has the following dual min 421 22 21 272 6 221 210 2 21 2... View the full answer