Please answer question 6

Consider the following problem: Maximize Z= subject to 3x1 + 2x2 2x1 - x2 X1 > 0, x2 > 0. 2 2 (1) (2) (a) Let M +00. Construct the big-M problem for the big-M method in augmented/tabular form by introducing slack, excess and/or artificial variables. Define all variables clearly. (b) Work through the tabular form of the big-M method to demonstrate that the problem has an unbounded Z. (a) Let si be the slack variable for constraint 1. Let ez be the excess variable for constraint 2. Let az be the artificial variable for constraint 2. EITHER: Big-M problem in algebraic form: Maximize Z= subject to 30 + 2:02 - Maz 2.11 - 12 + $i -21 + 22 - 2 + 2 21 > 0, 22 > 0, e2 > 0, si > 0, 0, > 0. = = 2 2 S102 RHS 0 M 0 1# 1# 2 -1 N No (b) OR: Big-M problem in tabular form:: BVZ 2 12 e2 Z 1 -3 - 2 0 Si 0 0 0 -1 1 -1 Iteration 0: BV Z - M M -3 -2 0 2 -1 0 0 -1 1* -1 -2M 0 0 1 0 0 0 0 1 Iteration 1: BVZ 222e28102 RHS 0 0 0 0 M 5 0 2 0 2 1* 0 -1 1 1 All coefficients of e2 are negative, thus Z is unbounded. Iteration 2 (NOT NECESSARY): 0 1 Z 1 0 0 -7 5 7 21 0 1 0 -1 1 1 122 0 0 1 - 2 1 21 All coefficients of e2 are negative, thus Z is unbounded. Question 6 (50%). Consider the following problem: Maximize Z= subject to 3x1 + 2x2 2x1 - x2 = -X1 + x2 > X1 > 0, x2 > 0. 2 2 (1) (2) (a) Let M +0. Construct the big-M problem for the big-M method in augmented/tabular form by introducing slack, excess and/or artificial variables. Define all variables clearly. (b) Work through the tabular form of the big-M method to demonstrate that the problem has an unbounded Z