Question: 1. The following questions below apply to the linear program maximize z= 3x1 + 13x2 + 13X3 subject to X1 + x2 0 with optimal

1. The following questions below apply to the

1. The following questions below apply to the linear program maximize z= 3x1 + 13x2 + 13X3 subject to X1 + x2 0 with optimal basis {X1, X2, X3} and 5/2 -3/2 B-1 = -3/2 3/2 1 -1 1 -1 1 All of the questions are independent. (i) What is the solution to the problem? What are the optimal dual variables? (ii) What is the solution of the linear program obtained by decreasing the right-hand side of the second constraint by 5? (iii) By how much can the right-hand side of the first constraint increase and decrease without changing the optimal basis? (iv) What is the solution of the linear program obtained by increasing the coefficient of x2 in the objective by 15? (v) By how much can the objective coefficient of x, increase and decrease without changing the optimal basis? (vi) Would the current basis remain optimal if a new variable X4 were added to the model with objective coefficient c4 = 5 and constraint coefficients A4 = (2,-1,5)T? (vii) Determine the solution of the linear program obtained by adding the constraint X1 X2 + 2x3 6. (ix) Determine the solution of the linear program obtained by adding the constraint X1 + X2 + x3 = 10

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