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1. Consider the following problem Minimize Z= X1+2X2, subject to 90 30 and (a) Solve this problem...
4.6-1.* Consider the following problem. Maximize Z= 2x1 + 3x2, subject to x1 + 2x2 54...
4.6-1.* Consider the following problem. Maximize Z= 2x1 + 3x2, subject to x1 + 2x2 54 x1 + x2 = 3 and X120, X2 0. DI (a) Solve this problem graphically. (b) Using the Big M method, construct the complete first simplex tableau for the simplex method and identify the corresponding initial (artificial) BF solution. Also identify the initial entering basic variable and the leaving basic variable. I (c) Continue from part (b) to work through the simplex method step...
2. Solve the LPP by the dual simplex method Minimize: z = 3x1 + 2x2 Subject...
2. Solve the LPP by the dual simplex method Minimize: z = 3x1 + 2x2 Subject to:: x1 + x2 > 1 4x1 + x2 > 2 -X1 + 2x2 < 6 Xi > 0, i=1,2
Consider the following problem Minimize Z3x+2 subject to 3+26 and 20, 20 ()Solve this problem graphically...
Consider the following problem Minimize Z3x+2 subject to 3+26 and 20, 20 ()Solve this problem graphically (b) Using the Big M method, construct the complete first simplex tableau for the simplex method and identify the corresponding initial (artificial) BF solution. Also identify the initial entering basic variable and the leaving basic variable. (c) Work through the simplex method step by step to solve the problem
[4.37] Consider the following problem: Maximize 2x + 3x2 subject to X1 + 2x2 5 10...
[4.37] Consider the following problem: Maximize 2x + 3x2 subject to X1 + 2x2 5 10 -*1 + 2x2 s 6 *1 + *2 S6 12 0. a. c. X1, Solve the problem graphically and verify that the optimal point is a degenerate basic feasible solution. b. Solve the problem by the simplex method. From Part (a), identify the constraint that causes degeneracy and resolve the problem after deleting this constraint. Note that degeneracy disappears and the same optimal solution...
Solve the following problems using the Simplex method and verify it graphically Problem 4 Minimize f=5x1...
Solve the following problems using the Simplex method and verify it graphically Problem 4 Minimize f=5x1 + 4x2 - 23 subject to X1 + 2x2 - X3 = 1 2x1 + x2 + x3 = 4 X1, X2 2 0; xz is unrestricted in sign
Consider the following Linear Problem Minimize 2x1 + 2x2 equation (1) subject to: x1 + x2...
Consider the following Linear Problem Minimize 2x1 + 2x2 equation (1) subject to: x1 + x2 >= 6 equation (2) x1 - 2x2 >= -18 equation (3) x1>= 0 equation (4) x2 >= 0 equation (5) 13. What is the feasible region for Constraint number 1, Please consider the Non-negativity constraints. 14. What is the feasible region for Constraint number 2, Please consider the Non-negativity constraints. 15. Illustrate (draw) contraint 1 and 2 in a same graph and find interception...
Use the simplex method to solve the linear programming problem. Maximize z= 7x1 + 2x2 + x3 subject to: x1...
Use the simplex method to solve the linear programming problem. Maximize z= 7x1 + 2x2 + x3 subject to: x1 + 4x2 + 8x3 ≤ 113 x1 + 2x2 + 10x3 ≤ 209 with x1 ≥ 0, x2 ≥ 0, x3 ≥ 0. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A.The maximum is ___ when x1 = ___, x2 =___, and x3 = ___. (Simplify your answers.) B.There is no...
2a. Consider the following problem. Maximize 17-Gri +80 Subject to 5x1 + 2x2 320 i 212 10 and Construct the dual problem for the above primal problem solve both the primal problem and the dual...
2a. Consider the following problem. Maximize 17-Gri +80 Subject to 5x1 + 2x2 320 i 212 10 and Construct the dual problem for the above primal problem solve both the primal problem and the dual problem graphically. Identify the corner- point feasible (CPF) solutions and comer-point infeasible solutions for both problems. Calculate the objective function values for all these values. Identify the optimal solution for Z. I 피 University 2b. For each of the following linear programming models write down...
Consider the following LPP: Maximize z = 50x1 + 20x2 + 30x3 subject to 2x1 + x2 + 3x3 + 90 (Resource A) x1 + 2x2 + x3 +...
Consider the following LPP: Maximize z = 50x1 + 20x2 + 30x3 subject to 2x1 + x2 + 3x3 + 90 (Resource A) x1 + 2x2 + x3 + 50 (Resource B) x1 + x2 + x3 + 80 (Resource C) x1, x2 , x3 > 0 The final simplex table is Basis cj x1 x2 x3 s1 s2 s3 Solution 50 20 30 0 0 0 x1 50 1 -1 0 1 -1 0 40 x3 30 0...
Consider the following linear program: Maximize Z-3xI+2x2-X3 Subject to:X1+X2+2 X3s 10 2x1-X2+X3 s20 3 X1+X2s15 X1, X2,...
Consider the following linear program: Maximize Z-3xI+2x2-X3 Subject to:X1+X2+2 X3s 10 2x1-X2+X3 s20 3 X1+X2s15 X1, X2, X320 (a) Convert the above constraints to equalities. (2 marks) (b) Set up the initial simplex tableau and solve. (9 marks)
Consider the following linear program: Maximize Z-3xI+2x2-X3 Subject to:X1+X2+2 X3s 10 2x1-X2+X3 s20 3 X1+X2s15 X1, X2, X320 (a) Convert the above constraints to equalities. (2 marks) (b) Set up the initial simplex tableau and solve. (9 marks)
4.6-1.* Consider the following problem. Maximize Z= 2x1 + 3x2, subject to x1 + 2x2 54 x1 + x2 = 3 and X120, X2 0. DI (a) Solve this problem graphically. (b) Using the Big M method, construct the complete first simplex tableau for the simplex method and identify the corresponding initial (artificial) BF solution. Also identify the initial entering basic variable and the leaving basic variable. I (c) Continue from part (b) to work through the simplex method step...
2. Solve the LPP by the dual simplex method Minimize: z = 3x1 + 2x2 Subject to:: x1 + x2 > 1 4x1 + x2 > 2 -X1 + 2x2 < 6 Xi > 0, i=1,2
Consider the following problem Minimize Z3x+2 subject to 3+26 and 20, 20 ()Solve this problem graphically (b) Using the Big M method, construct the complete first simplex tableau for the simplex method and identify the corresponding initial (artificial) BF solution. Also identify the initial entering basic variable and the leaving basic variable. (c) Work through the simplex method step by step to solve the problem
[4.37] Consider the following problem: Maximize 2x + 3x2 subject to X1 + 2x2 5 10 -*1 + 2x2 s 6 *1 + *2 S6 12 0. a. c. X1, Solve the problem graphically and verify that the optimal point is a degenerate basic feasible solution. b. Solve the problem by the simplex method. From Part (a), identify the constraint that causes degeneracy and resolve the problem after deleting this constraint. Note that degeneracy disappears and the same optimal solution...
Solve the following problems using the Simplex method and verify it graphically Problem 4 Minimize f=5x1 + 4x2 - 23 subject to X1 + 2x2 - X3 = 1 2x1 + x2 + x3 = 4 X1, X2 2 0; xz is unrestricted in sign
2a. Consider the following problem. Maximize 17-Gri +80 Subject to 5x1 + 2x2 320 i 212 10 and Construct the dual problem for the above primal problem solve both the primal problem and the dual problem graphically. Identify the corner- point feasible (CPF) solutions and comer-point infeasible solutions for both problems. Calculate the objective function values for all these values. Identify the optimal solution for Z. I 피 University 2b. For each of the following linear programming models write down...
Consider the following linear program: Maximize Z-3xI+2x2-X3 Subject to:X1+X2+2 X3s 10 2x1-X2+X3 s20 3 X1+X2s15 X1, X2, X320 (a) Convert the above constraints to equalities. (2 marks) (b) Set up the initial simplex tableau and solve. (9 marks)
Consider the following linear program: Maximize Z-3xI+2x2-X3 Subject to:X1+X2+2 X3s 10 2x1-X2+X3 s20 3 X1+X2s15 X1, X2, X320 (a) Convert the above constraints to equalities. (2 marks) (b) Set up the initial simplex tableau and solve. (9 marks)
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