Let consider the following linear program: Maximize Z=4x4 +6x, +3X, +X, Subject to: 1.5x + 2x2 + 4x3 +30x, 3550 ; 4x + xy + 2xy + x, S 700; 2x+3x2 + xy + 2x, 200: X, X, X, and x, 20. The final simplex tableau of this program is as follows: (constraint 1) (constraint 2) (constraint 3) CB Basis X S2 X2 X 4 0.05 3.25 0.65 4.05 -0.05 6 6 Zj Cj-Z; 6 0 0 1 6 0 X4 1 8.6 -14 -22 12.6 - 11.6 Si 0 0.3 -0.5 -0.1 0.3 -0.3 S2 0 0 1 0 Ss 0RHS -0.2 125 425 0.4 25 1.8 525 -1.8 where s, s, and sy represent the slack variables related to the constraints 1, 2 and 3 respectively. a. What is the impact on the objective function due to the production of one unit of productx,? Justify your answer by showing the changes in the RHS values of X3, s, and x(10 marks). b. How much are you willing to pay for additional resources related to the following constraints: (1) constraint 2 and (ii) constraint 3. Justify your answers by showing the changes in the RHS values of x3, 5, and x(10 marks). HINT: You can either derive your answers directly using the final simplex tableau or you can use Excel Solver (the excel files are not required). Let consider the following linear program: Maximize Z=4x, +6X, +3x2 + x4 Subject to: 1.5x + 2x2 + 4x3 +30x, 3550 ; 4x + xy + 2x, +x, S 700; 2xy + 3x2 + xy + 2x, 5200; X, X, X, and x, 20. The final simplex tableau of this program is as follows: (constraint 1) (constraint 2) (constraint 3) W X4 X 3 CB Basis X S2 X X 4 0.05 3.25 0.65 4.05 -0.05 6 6 Zj Cj-Z; 6 0 0 1 6 0 8.6 -14 -2.2 12.6 - 11.6 SI 0 0.3 -0.5 -0.1 0.3 -0.3 S2 0 0 1 0 S: 0RHS -0.2 125 425 0.4 25 1.8 525 -1.8 where s, s, and sy represent the slack variables related to the constraints 1, 2 and 3 respectively. a. What is the impact on the objective function due to the production of one unit of productx, ? Justify your answer by showing the changes in the RHS values of X3, s, and xz (10 marks). b. How much are you willing to pay for additional resources related to the following constraints: (1) constraint 2 and (ii) constraint 3. Justify your answers by showing the changes in the RHS values of x3, 5, and x (10 marks). HINT: You can either derive your answers directly using the final simplex tableau or you can use Excel Solver (the excel files are not required). Let consider the following linear program: Maximize Z=4x4 +6x, +3X, +X, Subject to: 1.5x + 2x2 + 4x3 +30x, 3550 ; 4x + xy + 2xy + x, S 700; 2x+3x2 + xy + 2x, 200: X, X, X, and x, 20. The final simplex tableau of this program is as follows: (constraint 1) (constraint 2) (constraint 3) CB Basis X S2 X2 X 4 0.05 3.25 0.65 4.05 -0.05 6 6 Zj Cj-Z; 6 0 0 1 6 0 X4 1 8.6 -14 -22 12.6 - 11.6 Si 0 0.3 -0.5 -0.1 0.3 -0.3 S2 0 0 1 0 Ss 0RHS -0.2 125 425 0.4 25 1.8 525 -1.8 where s, s, and sy represent the slack variables related to the constraints 1, 2 and 3 respectively. a. What is the impact on the objective function due to the production of one unit of productx,? Justify your answer by showing the changes in the RHS values of X3, s, and x(10 marks). b. How much are you willing to pay for additional resources related to the following constraints: (1) constraint 2 and (ii) constraint 3. Justify your answers by showing the changes in the RHS values of x3, 5, and x(10 marks). HINT: You can either derive your answers directly using the final simplex tableau or you can use Excel Solver (the excel files are not required). Let consider the following linear program: Maximize Z=4x, +6X, +3x2 + x4 Subject to: 1.5x + 2x2 + 4x3 +30x, 3550 ; 4x + xy + 2x, +x, S 700; 2xy + 3x2 + xy + 2x, 5200; X, X, X, and x, 20. The final simplex tableau of this program is as follows: (constraint 1) (constraint 2) (constraint 3) W X4 X 3 CB Basis X S2 X X 4 0.05 3.25 0.65 4.05 -0.05 6 6 Zj Cj-Z; 6 0 0 1 6 0 8.6 -14 -2.2 12.6 - 11.6 SI 0 0.3 -0.5 -0.1 0.3 -0.3 S2 0 0 1 0 S: 0RHS -0.2 125 425 0.4 25 1.8 525 -1.8 where s, s, and sy represent the slack variables related to the constraints 1, 2 and 3 respectively. a. What is the impact on the objective function due to the production of one unit of productx, ? Justify your answer by showing the changes in the RHS values of X3, s, and xz (10 marks). b. How much are you willing to pay for additional resources related to the following constraints: (1) constraint 2 and (ii) constraint 3. Justify your answers by showing the changes in the RHS values of x3, 5, and x (10 marks). HINT: You can either derive your answers directly using the final simplex tableau or you can use Excel Solver (the excel files are not required)