![2. Consider the problem 51 2 3 1 07-131 x>0, XA + x3 = min. [4 5 6 0 1]+=9]: ** Start with the feasible solution tº = [0,0,0,](http://img.homeworklib.com/questions/1a107e80-31bd-11eb-b089-03f35f7b093f.png?x-oss-process=image/resize,w_560)
Homework Answers
2. Consider the problem 51 2 3 1 07-131 x>0, XA + x3 = min. [4 5 6 0 1]+=9]: ** Start with the feasible solution tº = [0,0,0,3,9]
Consider the following linear program min -10.01 - 3.02 x1 + x2 + x3 = 4...
Consider the following linear program min -10.01 - 3.02 x1 + x2 + x3 = 4 5x 1 + 2x2 + x4 = 11 Z2 + 5 = 4 21,22,23,24,25 > 0 (a) Starting from the basis B = {2,3,4}, solve the linear program using the simplex method. (b) Removing the slack variables, we have the equivalent formulation. min -10:31 - 322 21 +224 5.11 + 2.22 <11 1 x2 < 4 21,220 Plot the feasible region and mark the...
Question 1 - Revised Simplex Algorithm 10 marks Suppose we are solving the following linear programming problem Subject...
Question 1 - Revised Simplex Algorithm 10 marks Suppose we are solving the following linear programming problem Subject to 8x1 + 12x2 + x3 15x2 + x4 3x1 + 6x2 + X5 -120 60 = 48 x1,x2,x3, x4,x5 2 0 Assume we have a current basis of x2,xz, x5. Demonstrate your understanding of the steps of the Revised Simplex Algorithm by answering the following: a) What is the basic feasible solution at this stage? What is the value of the...
SOLVE STEP BY STEP! 4. Consider the following LP: Minimize z = x; +3x2 - X3...
SOLVE STEP BY STEP!
4. Consider the following LP: Minimize z = x; +3x2 - X3 Subject to x + x2 + x2 > 3 -x + 2xz > 2 -x + 3x2 + x3 34 X1 X2,43 20 (a) Using the two-phase method, find the optimal solution to the primal problem above. (b) Write directly the dual of the primal problem, without using the method of transformation. (c) Determine the optimal values of the dual variables from the optimal...
1. Solving the linear programming problem Maximize z 3r1 2r2 3, subject to the constraints using ...
1. Solving the linear programming problem Maximize z 3r1 2r2 3, subject to the constraints using the simplex algorithm gave the final tableau T4 T5 #210 1-1/4 3/8-1/812 0 0 23/4 3/8 7/8 10 (a) (3 points) Add the constraint -221 to the final tableau and use the dual simplex algorithm to find a new optimal solution. (b) (3 points) After adding the constraint of Part (a), what happens to the optimal solution if we add the fourth constraint 2+...
16.10 Consider the linear programming problem minimze -T subject to 1-2-1 T1,2 20 a. Write down the basic feasible solu...
16.10 Consider the linear programming problem minimze -T subject to 1-2-1 T1,2 20 a. Write down the basic feasible solution for z as a basic variable. b. Compute the canonical augmented matrix corresponding to the basis in part a c. If we apply the simplex algorithm to this problem, under what circum stance does it terminate? (In other words, which stopping criterion in the simplex algorithm is satisfied?) d. Show that in this problem, the objective function can take arbitrarily...
[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...
2- The following linear programming problem maximizes the profit in a manufacturing setup. Suppose that the...
2- The following linear programming problem maximizes the profit in a manufacturing setup. Suppose that the first and second constraints show the labor and material constraint, respectively max z = 4x + 3x, +5x, S.T. x + 2x + 3x, 39 +3x, + x, 312 *.*, 20 Optimal table: NS RHS 6/5 X3 1/5 2/5 -1/5 3/5 X1 -1/5 27/5 O 18/5 6/5 - 1) Fill the blank cells in the table using Simplex Matrix Math. 2) Find the range...
Consider the following linear program: Min 3A + 48 +28 26 AB 20 2. Select the...
Consider the following linear program: Min 3A + 48 +28 26 AB 20 2. Select the correct graph that shows the feasible region and the optimal solution for the problem. 0 (1) 10 8 Optimal Solution: A-2, B-2 - Optional Solution And, BM A (iv) Optimal Solution: A-0, B- Optimal Solution: A=2, B-2 b. What is the value of the objective function? If required, round your answer to one decimal place. Objective function value:
Consider the linear program: 1, 2,3, 4,25 2 0 Perform a Phase-I calculation to determine an initi...
Consider the linear program: 1, 2,3, 4,25 2 0 Perform a Phase-I calculation to determine an initial basic feasible solution. Write down the initial simplex tableau for the Phase-I problem and the resulting initial simplex tableau for the Phase II problem. The initial simplex tableau must have the objective function expressed in terms of the nonbasic variables. You may use software to solve the Phase-I problem.
Consider the linear program: 1, 2,3, 4,25 2 0 Perform a Phase-I calculation to...
Problem 1 (20 pts) Consider the mathematical program max 3x1+x2 +3x3 s.t. 2x1 +x2 + x3 +x2 x1 + 2x2 + 3x3 +2xs 5 2x 2x2 +x3 +3x6-6 Xy X2, X3, X4, Xs, X620 Three feasible solutions ((a) through (c...
Problem 1 (20 pts) Consider the mathematical program max 3x1+x2 +3x3 s.t. 2x1 +x2 + x3 +x2 x1 + 2x2 + 3x3 +2xs 5 2x 2x2 +x3 +3x6-6 Xy X2, X3, X4, Xs, X620 Three feasible solutions ((a) through (c)) are listed below. (0.3, 0.1, 0.4, 0.9, 1.65, 1.6) (c) x Please choose one appropriate interior point from the list, and use the Karmarkar's Method at the interior point and determine the optimal solution. 25
Problem 1 (20 pts) Consider...
Consider the following linear program min -10.01 - 3.02 x1 + x2 + x3 = 4 5x 1 + 2x2 + x4 = 11 Z2 + 5 = 4 21,22,23,24,25 > 0 (a) Starting from the basis B = {2,3,4}, solve the linear program using the simplex method. (b) Removing the slack variables, we have the equivalent formulation. min -10:31 - 322 21 +224 5.11 + 2.22 <11 1 x2 < 4 21,220 Plot the feasible region and mark the...
Question 1 - Revised Simplex Algorithm 10 marks Suppose we are solving the following linear programming problem Subject to 8x1 + 12x2 + x3 15x2 + x4 3x1 + 6x2 + X5 -120 60 = 48 x1,x2,x3, x4,x5 2 0 Assume we have a current basis of x2,xz, x5. Demonstrate your understanding of the steps of the Revised Simplex Algorithm by answering the following: a) What is the basic feasible solution at this stage? What is the value of the...
SOLVE STEP BY STEP!
4. Consider the following LP: Minimize z = x; +3x2 - X3 Subject to x + x2 + x2 > 3 -x + 2xz > 2 -x + 3x2 + x3 34 X1 X2,43 20 (a) Using the two-phase method, find the optimal solution to the primal problem above. (b) Write directly the dual of the primal problem, without using the method of transformation. (c) Determine the optimal values of the dual variables from the optimal...
1. Solving the linear programming problem Maximize z 3r1 2r2 3, subject to the constraints using the simplex algorithm gave the final tableau T4 T5 #210 1-1/4 3/8-1/812 0 0 23/4 3/8 7/8 10 (a) (3 points) Add the constraint -221 to the final tableau and use the dual simplex algorithm to find a new optimal solution. (b) (3 points) After adding the constraint of Part (a), what happens to the optimal solution if we add the fourth constraint 2+...
16.10 Consider the linear programming problem minimze -T subject to 1-2-1 T1,2 20 a. Write down the basic feasible solution for z as a basic variable. b. Compute the canonical augmented matrix corresponding to the basis in part a c. If we apply the simplex algorithm to this problem, under what circum stance does it terminate? (In other words, which stopping criterion in the simplex algorithm is satisfied?) d. Show that in this problem, the objective function can take arbitrarily...
[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...
2- The following linear programming problem maximizes the profit in a manufacturing setup. Suppose that the first and second constraints show the labor and material constraint, respectively max z = 4x + 3x, +5x, S.T. x + 2x + 3x, 39 +3x, + x, 312 *.*, 20 Optimal table: NS RHS 6/5 X3 1/5 2/5 -1/5 3/5 X1 -1/5 27/5 O 18/5 6/5 - 1) Fill the blank cells in the table using Simplex Matrix Math. 2) Find the range...
Consider the following linear program: Min 3A + 48 +28 26 AB 20 2. Select the correct graph that shows the feasible region and the optimal solution for the problem. 0 (1) 10 8 Optimal Solution: A-2, B-2 - Optional Solution And, BM A (iv) Optimal Solution: A-0, B- Optimal Solution: A=2, B-2 b. What is the value of the objective function? If required, round your answer to one decimal place. Objective function value:
Consider the linear program: 1, 2,3, 4,25 2 0 Perform a Phase-I calculation to determine an initial basic feasible solution. Write down the initial simplex tableau for the Phase-I problem and the resulting initial simplex tableau for the Phase II problem. The initial simplex tableau must have the objective function expressed in terms of the nonbasic variables. You may use software to solve the Phase-I problem.
Consider the linear program: 1, 2,3, 4,25 2 0 Perform a Phase-I calculation to...
Problem 1 (20 pts) Consider the mathematical program max 3x1+x2 +3x3 s.t. 2x1 +x2 + x3 +x2 x1 + 2x2 + 3x3 +2xs 5 2x 2x2 +x3 +3x6-6 Xy X2, X3, X4, Xs, X620 Three feasible solutions ((a) through (c)) are listed below. (0.3, 0.1, 0.4, 0.9, 1.65, 1.6) (c) x Please choose one appropriate interior point from the list, and use the Karmarkar's Method at the interior point and determine the optimal solution. 25
Problem 1 (20 pts) Consider...
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