Question: Problem 2: This is based on Problem 10 of the review problems in Section 6 of the textbook by 'Winston and Venkataraman. Consider the following

Problem 2: This is based on Problem 10 of the review problems in Section 6 of the textbook by 'Winston and Venkataraman. Consider the following LP and its optimal tableau: max 2' = 3331 + 233-; st. 2-111 5132 g 8 3331 -- 73132 g 10 $1,312 2 0 2' 3:1 3:2 .31 82 rhs 1 O 5 O 1 10 0 O 1/3 1 2/3 4/3 0 1 7/3 0 1/3 10/3 Note, the constraint matrix for basic variable this problem is only 2 by 2. Thus3 it is not too hard to do matrix inversion. Please solve this problem using matrix operations only. (a) Find the dual of this LP and its optimal solution (b) Find the range of values of 12 (rhs of second constraint) for which the current primal basis remains optimal. Also nd the new optimal solution if 52 = 5. (c) Change the objective function of the given (primal) LP so that its dual becomes infeasible, orargue why this cannot be done

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