5. Solve the linear program below as follows: First, solve the dual problem graphically. Then use...
(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...
(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. 8. Minimize z -8x1 + 6x2 + 11x3 subject to 5x1 x2 + 3x3 s 4 5x1 + x2 + 3x3「2 2x1 + 4x2 + 7x3 s.5 2x1 + 4x2 + 7x3 2 3 x1 + x2...
Problem #5 -- Consider the following linear programming problem: Maximize Z = 2x1 + 4x2 + 3x3 subject to: X1 + 3x2 + 2x3 S 30 best to X1 + x2 + x3 S 24 3x1 + 5x2 + 3x3 5 60 and X120, X220, X3 2 0. You are given the information that x > 0, X2 = 0, and x3 >O in the optimal solution. Using the given information and the theory of the simplex method, analyze the...
Use the Gaussian elimination method to solve each of the following systems of linear equations. In each case, indicate whether the system is consistent or inconsistent. Give the complete solution set, and if the solution set is infinite, specify three particular solutions. 1-5x1 – 2x2 + 2x3 = 14 *(a) 3x1 + x2 – x3 = -8 2x1 + 2x2 – x3 = -3 3x1 – 3x2 – 2x3 = (b) -6x1 + 4x2 + 3x3 = -38 1-2x1 +...
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 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...
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...
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 ...
#4 What is the dual of the following linear programing I problem: not solve maximize X1 + 2x2 - X3 + X₂ A:X + 3x2 + 4xz - 2x4 63 - x - x2 + 2x3 + x4 = 1. X, 2, tz & O.