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Question 4: (25 points) (This question can be solved in 15 minutes easily) Consider the following original LP The artificial standard form of the above model is given model. below. Max z= -4X1 + X2-5X3 + 3X4 Max z=-4X1 + X2 - 5X3 + 3X4 - MA2 - MA3 s.t. s.t. -X1 + 2X2 + X4 = 50 -X1 + 2X2 + X4 + A1 = 50 2X2 + X3 2X2 + X3 > 40 3X1 + X2 - 2x3 + 4X4 0 The following Simplex Table shows the optimal solution of the above model. Basis X1 X2 X3 X4 A1 E2 A2 S3 RHS Z 1 0 5/2 0 (M+3) 5/2 (M-5/2) 0 50 X4 - 1 0 - 1 1 1 1 - 1 0 10 X2 0 1 1/2 0 0 -1/2 1/2 0 20 S3 7 0 3/20 -4 -7/2 7/2 1 40 a) For which values of the RHS constant of the third constraint (b) the above basis gives the optimal solution? b) For which values of the objective function coefficient of X1 (Ci) the above basis gives the optimal solution