Problem 2 The following LP starts at an infeasible basis. Follow the steps to use the...

Transcribed Image Text:

Problem 2 The following LP starts at an infeasible basis. Follow the steps to use the Two- Phased-Simplex algorithm and find a feasible basic solution. Minimize x1 x2 s.t. x13x26 5x12x210 x24 X 0 (a) Put the model in the canonical form for the basis {81, 82, 83}. The associated solution should be infeasible. How can we tell? (b) Create the phase one LP by subtracting an auxiliary variable (a1 and a2) from each of the con- straints that have negative right-hand-side and replacing the objective function with "Maximize -a1a2." (c) Pivot your phase one LP into the basis B = {a1, a2, 83}. This should be a feasible basis. (d) Use the simplex method to find the optimal solution to the phase one LP. It should take two pivots. Report the basis and canonical form for each pivot in addition to your optimal solution. Does this solution represent a feasible solution to the original LP? How do you know? (e) Now that we have a feasible basis, solve the original LP to optimality. Problem 2 The following LP starts at an infeasible basis. Follow the steps to use the Two- Phased-Simplex algorithm and find a feasible basic solution. Minimize x1 x2 s.t. x13x26 5x12x210 x24 X 0 (a) Put the model in the canonical form for the basis {81, 82, 83}. The associated solution should be infeasible. How can we tell? (b) Create the phase one LP by subtracting an auxiliary variable (a1 and a2) from each of the con- straints that have negative right-hand-side and replacing the objective function with "Maximize -a1a2." (c) Pivot your phase one LP into the basis B = {a1, a2, 83}. This should be a feasible basis. (d) Use the simplex method to find the optimal solution to the phase one LP. It should take two pivots. Report the basis and canonical form for each pivot in addition to your optimal solution. Does this solution represent a feasible solution to the original LP? How do you know? (e) Now that we have a feasible basis, solve the original LP to optimality.