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Linear Programming Problems 1. Write the basic feasible solution from the tableau given here. 5 0...
The following simplex tableau is in final form. Find the basic feasible solution to the linear...
The following simplex tableau is in final form. Find the basic feasible solution to the linear programming problem associated with this tableau. 12 y 24 WP Constant 0 1/2 0 1 -1/2 0 0 To 1/4 1 0 5/4 -1/2 0 11 1 1/4 0 0 -3/4 1/2 0 LO 13 0 0 4 1/2 1
3.4 EXERCISES In Exercises 1-5 the given tableau represents a solution to a linear programming pr...
3.4 EXERCISES In Exercises 1-5 the given tableau represents a solution to a linear programming problem that satisfies the optimality criterion, but is infeasible. Use the dual simplex method to restore feasibility 0x 0001 0 0 0x 1000-0 3'00-00 C. 0730 5
3.4 EXERCISES In Exercises 1-5 the given tableau represents a solution to a linear programming problem that satisfies the optimality criterion, but is infeasible. Use the dual simplex method to restore feasibility
0x 0001 0 0 0x 1000-0...
For the given simplex tableau, (a) list the basic and the nonbasic variables, (b) find the basic feasible solution determined by setting the nonbasic variables equal to 0, and (c) decide wh...
For the given simplex tableau, (a) list the basic and the nonbasic variables, (b) find the basic feasible solution determined by setting the nonbasic variables equal to 0, and (c) decide whether this is a maximum solution. x 1x1 x 2x2 x 3x3 s 1s1 s 2s2 zz 77 00 22 negative 1−1 11 00 2525 22 11 00 negative 3−3 00 00 1818 negative 8−8 00 negative 2−2 negative 1−1 00 11 1111 (a) What are the basic variables?...
b. Given the following tableau find an alternative basic feasible optimal solution. (10 pts) 2 X,...
b. Given the following tableau find an alternative basic feasible optimal solution. (10 pts) 2 X, X2 X3 X4 X5 X6 RHS 2 1 0 0 0 0 2 3 4 X 0 1 0 2 -1 -1 1 2 X, 0 0 -2 2 3 2
The initial and final tableaus of a linear-programming problems are as follows: Initial Tableau B...
The initial and final tableaus of a linear-programming problems are as follows: Initial Tableau Basic variables | values | X1 | X2 | X3 | X4 | X5 | X6 rs 710 1 1340 (H2) 12 20 18 40 1 Final Tableau Current Basic variables valuesi r6 TSI-TS r1 150 30 10 x4 15 30 131 (5 Verify the complementary-slackness conditions. m n aiix i i Vi, j=1
The initial and final tableaus of a linear-programming problems are as follows:...
Corollary 8. For any pair of feasible solutions of dual canonical linear programming problems, we have...
Corollary 8. For any pair of feasible solutions of dual canonical linear programming problems, we have 14. State and prove the analogue of Corollary 8 for dual noncanonical linear programming problems.
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...
The initial tableau of a linear programming problem is given. Use the simplex method to solve...
The
initial tableau of a linear programming problem is given. Use the
simplex method to solve it.
X1 X2 x3 S1 S2 z 1-0여 8 3 8 1 0 110 -3 -24 1 0 0 0
Introduce slack variables as necessary and then write the initial simplex tableau for the given linear...
Introduce slack variables as necessary and then write the initial simplex tableau for the given linear programming problem. Complete the initial simplex tableau. 1 1 X, X2 X3 s, 3 8 5 0 2 2 0 0 ONN S2 S3 0 0 0 0 0 0 NOOO 1 12 9 9 1 0 Z= X1 +8X2 +3X3 Maximize subject to X1 8X4 +2x2 +X2 +3x3 12 + 5x3 39 + 2x3 = 9 20, X3 20. 2x X1 20, X2
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+...
The following simplex tableau is in final form. Find the basic feasible solution to the linear programming problem associated with this tableau. 12 y 24 WP Constant 0 1/2 0 1 -1/2 0 0 To 1/4 1 0 5/4 -1/2 0 11 1 1/4 0 0 -3/4 1/2 0 LO 13 0 0 4 1/2 1
3.4 EXERCISES In Exercises 1-5 the given tableau represents a solution to a linear programming problem that satisfies the optimality criterion, but is infeasible. Use the dual simplex method to restore feasibility 0x 0001 0 0 0x 1000-0 3'00-00 C. 0730 5
3.4 EXERCISES In Exercises 1-5 the given tableau represents a solution to a linear programming problem that satisfies the optimality criterion, but is infeasible. Use the dual simplex method to restore feasibility
0x 0001 0 0 0x 1000-0...
b. Given the following tableau find an alternative basic feasible optimal solution. (10 pts) 2 X, X2 X3 X4 X5 X6 RHS 2 1 0 0 0 0 2 3 4 X 0 1 0 2 -1 -1 1 2 X, 0 0 -2 2 3 2
The initial and final tableaus of a linear-programming problems are as follows: Initial Tableau Basic variables | values | X1 | X2 | X3 | X4 | X5 | X6 rs 710 1 1340 (H2) 12 20 18 40 1 Final Tableau Current Basic variables valuesi r6 TSI-TS r1 150 30 10 x4 15 30 131 (5 Verify the complementary-slackness conditions. m n aiix i i Vi, j=1
The initial and final tableaus of a linear-programming problems are as follows:...
Corollary 8. For any pair of feasible solutions of dual canonical linear programming problems, we have 14. State and prove the analogue of Corollary 8 for dual noncanonical linear programming problems.
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...
The
initial tableau of a linear programming problem is given. Use the
simplex method to solve it.
X1 X2 x3 S1 S2 z 1-0여 8 3 8 1 0 110 -3 -24 1 0 0 0
Introduce slack variables as necessary and then write the initial simplex tableau for the given linear programming problem. Complete the initial simplex tableau. 1 1 X, X2 X3 s, 3 8 5 0 2 2 0 0 ONN S2 S3 0 0 0 0 0 0 NOOO 1 12 9 9 1 0 Z= X1 +8X2 +3X3 Maximize subject to X1 8X4 +2x2 +X2 +3x3 12 + 5x3 39 + 2x3 = 9 20, X3 20. 2x X1 20, X2
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+...
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