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Problem 3: Complentary slackness From Deterministic Operations Research, David J. Rader, Jr. Supp...
Problem 3: Complentary slackness From Deterministic Operations Research, David J. Rader, Jr. Suppose that xı -2,...
Problem 3: Complentary slackness From Deterministic Operations Research, David J. Rader, Jr. Suppose that xı -2, r2 0, T3 -4 is an optimal solution to the linear program: max 4x1 + 2x2 + 3x3 s.t. 2x1+3x2 +x3 12 1 4r2 2x3 10 3zi 23 10 2x1 +3x2 +t3 12 21, 32,c3 20 (a) Using only the primal solution, complementary slackness, and the strong duality theorem, find an optimal solution to the dual problem. (b) Write the dual LP of this...
Duality Theory : Consider the following LP problem: Maximize Z = 2x1 + x2 - x3...
Duality Theory : Consider the following LP problem: Maximize Z = 2x1 + x2 - x3 subject to 2x1 + x2+ x3 ≤ 8 4x1 +x2 - x3 ≤ 10 x1 ≥ 0, x2 ≥ 0, x3 ≥ 0. (a) Find the dual for this LP (b) Graphically solve the dual of this LP. And interpret the economic meaning of the optimal solution of the dual. (c) Use complementary slackness property to solve the max problem (the primal problem). Clearly...
5. Solve the linear program below as follows: First, solve the dual problem graphically. Then use...
Operations Research
5. Solve the linear program below as follows: First, solve the dual problem graphically. Then use the solution to the dual problem to determine which variables in the primal problem are zero in the optimal primal solution. [Hint: Invoke complementary slackness.] Finally, solve for the optimal basic variables in the primal, using the primal equations. Primal Maximize-4x2 + 3x3 2x4-8xs, subject to: 3x1 + x2 + 2x3 +x4 = 3. x)2。 (j=1,2,3, 4.5).
5. Solve the linear program...
Solving an LP problem using complementary slackness
Solve the dual of the following L.P problem by simplex method. Hence find the solution of the primal using complimentary slackness conditions. Minimize Z = 4X1 - 5X2 - 2X3 Subject to 6X1 + X2 - X3 ≤ 5 2X1 + 2X2 - 3X3 ≥ 3 ...
(a) State the dual problem. (b) Solve both the primal and the dual problem with any method that w...
(a) State the dual problem.
(b) Solve both the primal and the dual problem with any method
that works.
(c) Check that your optimal solutions are correct by verifying they
are feasible and the primal and dual objective functions give the
same value.
9. Minimize z subject to 4x1 + x2 + x3 + 3x4 2x, + x2 + 3x3 + x4 2 12 3xi + 2x2 + 4x3 2x1-x2 + 2x3 + 3x4-8 3x1 + 4x2 + 3x3 х,2...
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...
Probs. 3-4-5 refer to the following problem and its complete solution Max . Z 4x1 + 6x2 + 3x3 + x+ ?2x1 + 2x2...
Probs. 3-4-5 refer to the following problem and its complete solution Max . Z 4x1 + 6x2 + 3x3 + x+ ?2x1 + 2x2 + 4x3 + 3x+ 550 (x5) 2x1 + 3x2 + x3 + 2x‘ S 20O (x7) R.S 4-6 -31 /4 3 1 550 700 200 0 o1 3 o 2 Z O 400 2/11 1/12/10 o 1/11 662 / ง 9 525 2 /20 425 2/ 25 1/2-1/10 13/20 1 0 。 3a. Read off the...
Given the following LP problem formulation and output data, perform the analysis below. Max. 100X1 +...
Given the following LP problem formulation and output data, perform the analysis below. Max. 100X1 + 120X2 + 150X3 + 125X4 s.t X1 + 2X2 + 2X3 + 2X4 < 108 (C1) 3X1 + 5X2 + X4 < 120 (C2) X1 + X3 < 25 (C3) X2 + X3 + X4 > 50 (C4) OPTIMAL SOLUTION: Objective Function Value = 7475.000 Variable Value Reduced Costs X1 8.000 0.500 X2 0.000 5.000 X3 17.000 0.000 X4 *A...
This is question 5.3-5 from Introduction to Operations Research (Hillier). Relevant text: Consider the following problem....
This is question 5.3-5 from Introduction to Operations Research
(Hillier). Relevant text:
Consider the following problem. Maximize Z= cixi + c2x2 + C3X3 subject to x1 + 2x2 + x3 = b 2x1 + x2 + 3x3 = 2b and x 20, X220, X2 > 0. Note that values have not been assigned to the coefficients in the objective function (C1, C2, C3). and that the only specification for the right-hand side of the functional constraints is that the second...
Problem 3: Complentary slackness From Deterministic Operations Research, David J. Rader, Jr. Suppose that xı -2, r2 0, T3 -4 is an optimal solution to the linear program: max 4x1 + 2x2 + 3x3 s.t. 2x1+3x2 +x3 12 1 4r2 2x3 10 3zi 23 10 2x1 +3x2 +t3 12 21, 32,c3 20 (a) Using only the primal solution, complementary slackness, and the strong duality theorem, find an optimal solution to the dual problem. (b) Write the dual LP of this...
Operations Research
5. Solve the linear program below as follows: First, solve the dual problem graphically. Then use the solution to the dual problem to determine which variables in the primal problem are zero in the optimal primal solution. [Hint: Invoke complementary slackness.] Finally, solve for the optimal basic variables in the primal, using the primal equations. Primal Maximize-4x2 + 3x3 2x4-8xs, subject to: 3x1 + x2 + 2x3 +x4 = 3. x)2。 (j=1,2,3, 4.5).
5. Solve the linear program...
(a) State the dual problem.
(b) Solve both the primal and the dual problem with any method
that works.
(c) Check that your optimal solutions are correct by verifying they
are feasible and the primal and dual objective functions give the
same value.
9. Minimize z subject to 4x1 + x2 + x3 + 3x4 2x, + x2 + 3x3 + x4 2 12 3xi + 2x2 + 4x3 2x1-x2 + 2x3 + 3x4-8 3x1 + 4x2 + 3x3 х,2...
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...
Probs. 3-4-5 refer to the following problem and its complete solution Max . Z 4x1 + 6x2 + 3x3 + x+ ?2x1 + 2x2 + 4x3 + 3x+ 550 (x5) 2x1 + 3x2 + x3 + 2x‘ S 20O (x7) R.S 4-6 -31 /4 3 1 550 700 200 0 o1 3 o 2 Z O 400 2/11 1/12/10 o 1/11 662 / ง 9 525 2 /20 425 2/ 25 1/2-1/10 13/20 1 0 。 3a. Read off the...
This is question 5.3-5 from Introduction to Operations Research
(Hillier). Relevant text:
Consider the following problem. Maximize Z= cixi + c2x2 + C3X3 subject to x1 + 2x2 + x3 = b 2x1 + x2 + 3x3 = 2b and x 20, X220, X2 > 0. Note that values have not been assigned to the coefficients in the objective function (C1, C2, C3). and that the only specification for the right-hand side of the functional constraints is that the second...
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