2. (40 points) Consider the LP in SEF with 1 2 3 4 A = =...

 

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2. (40 points) Consider the LP in SEF with 1 2 3 4 A = = 3 1 25 ' (1755), 6= 87 Start with the basis {1,3} and solve this LP to optimality by the sim- plex method. Show clearly all the data that is required in the previous question. In this question we do not tell you which are the entering variables. In each step, display the following: . The current basis and . AB, CB. For the canonical form: AB, y, cT - y A, the matrix AA and Ab. (If the problem is already in canonical form, then you do not need to compute these.) For clarity: rewrite the entire problem in canonical form as - max z(x) = yb + (cT y A)x s.t. AAx = Ab x 0. (2) If the solution is optimal, then conclude that. If it is not optimal, then specify i) the inequalities that limit how large the entering variable can be ii) the variable that leaves the basis. Write down the new solution. 2. (40 points) Consider the LP in SEF with 1 2 3 4 A = = 3 1 25 ' (1755), 6= 87 Start with the basis {1,3} and solve this LP to optimality by the sim- plex method. Show clearly all the data that is required in the previous question. In this question we do not tell you which are the entering variables. In each step, display the following: . The current basis and . AB, CB. For the canonical form: AB, y, cT - y A, the matrix AA and Ab. (If the problem is already in canonical form, then you do not need to compute these.) For clarity: rewrite the entire problem in canonical form as - max z(x) = yb + (cT y A)x s.t. AAx = Ab x 0. (2) If the solution is optimal, then conclude that. If it is not optimal, then specify i) the inequalities that limit how large the entering variable can be ii) the variable that leaves the basis. Write down the new solution.