4.4. The following questions below apply to the linear program minimize subject to z=-101x1 + 87x2...

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4.4. The following questions below apply to the linear program minimize subject to z=-101x1 + 87x2 +23x3 6x1-13x2 3x3 11 6x1 +11x2+2x3 45 x1+5x2+x3 12 X1, X2, X30 with optimal basic solution basic x1x2 X3 X3 X4 x5 rhs -2 0 0 0 12 4 5 372 x1 0 1 -2 7 x2 0 1 0 -4 9 -30 x3 0 0 1 19 -43 144 512 5 All of the questions are independent. (i) What is the solution of the linear program obtained by decreasing the right-hand side of the second constraint by 15? (ii) By how much can the right-hand side of the second constraint increase and decrease without changing the optimal basis? (iii) What is the solution of the linear program obtained by increasing the coefficient of x, in the objective by 25? (iv) By how much can the objective coefficient of x3 increase and decrease without changing the optimal basis? (v) Would the current basis remain optimal if a new variable x4 were added to the model with objective coefficient c4 = 46 and constraint coefficients A4 (12,-14, 15)? == (vi) Determine the solution of the linear program obtained by adding the constraint 5x1+7x2+9x3 50. 4.4. The following questions below apply to the linear program minimize subject to z=-101x1 + 87x2 +23x3 6x1-13x2 3x3 11 6x1 +11x2+2x3 45 x1+5x2+x3 12 X1, X2, X30 with optimal basic solution basic x1x2 X3 X3 X4 x5 rhs -2 0 0 0 12 4 5 372 x1 0 1 -2 7 x2 0 1 0 -4 9 -30 x3 0 0 1 19 -43 144 512 5 All of the questions are independent. (i) What is the solution of the linear program obtained by decreasing the right-hand side of the second constraint by 15? (ii) By how much can the right-hand side of the second constraint increase and decrease without changing the optimal basis? (iii) What is the solution of the linear program obtained by increasing the coefficient of x, in the objective by 25? (iv) By how much can the objective coefficient of x3 increase and decrease without changing the optimal basis? (v) Would the current basis remain optimal if a new variable x4 were added to the model with objective coefficient c4 = 46 and constraint coefficients A4 (12,-14, 15)? == (vi) Determine the solution of the linear program obtained by adding the constraint 5x1+7x2+9x3 50.