Question: Question 6 (50%). Consider the following problem, where the value of k (- 2 X1 > 0, x2 > 0, X3 > 0. (1) (2)

Question 6 (50%). Consider the following problem,

Question 6 (50%). Consider the following problem, where the value of k (- 2 X1 > 0, x2 > 0, X3 > 0. (1) (2) (a) Let M + 0. Let si be the slack variable for the constraint 1. Let e2 and az be the excess and artificial variables, respectively, for the constraint 2. Construct the initial big-M simplex tableau in canonical form in terms of k. (b) Identify Ls, X, C, A, b and Zo of the matrix equation for the initial simplex tableau in terms of k. X2 for the problem. Show by the fundamental insight (c) You are now given a basis XB that the corresponding y and S are: 21 y = [5, M 3], s = = [11] 2 -1 (d) Using the results in (c), construct the corresponding big-M simplex tableau in terms of k by the fundamental insight. Show all calculations. (e) Using the results in (d), find the range of k if the above xb is NOT an optimal basis

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