3. For the following linear programming (primal) problem Minimize Z -3x1 x2 - 2x3, subject to xx2...
(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...
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...
Linear programming question minimize 2x1 + 322 + 423, subject to 3x1-4x2-5x3 2 6, x1 +x2 +x3 = 10 Eliminate the equality constraint by replacing r in terms of ri, 22, and convert it into an equivalent LP with only inequality constraints. Then find a minimizer(エ4,2 for this LP.
Solve the following linear programming problem using Two Phase method [12M] Maximize z = 3X1 - 3X2 + X3 Subject to X; + 2x, - xz 25 - 3x; – x2 + x3 54 47, X2, X3 20.
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...
2x1 + 4x2 + 7x3 c1: x1 +x2 +x3 ≤ 105 c2: 3x1 +4x2 +2x3 ≥ 310 c3: 2x1 +4x2 +4x3 ≥ 330 x1,x2,x3 ≥ 0 The problem was solved using a computer program and the following output was obtained variabel value reduced cost allowable increase decrease x1 0.0 -3.5 3.5 inf x2 55 0 5 7 x3 60 0 inf 5 constraint slack/surplus dual price 1 0 10 2 0 -2 3 95 0 Constraint right-hand side sensitivity constraint...
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...
Based on this linear programming problem below, and answer the following questions: Minimize subject to Z=500 y, + 200 y, 3y, + y 24 -y, +2y, 210 y; - y, 215 -y, +4y, 225 y, 20, y, 20 and 1) Find the dual to the linear programming problem. 2) Using the simplex method to solve the dual problem. 3) The simplex method in part 2) should require 3 pivots (4 tableaus including the initial one). For each tableau, write the...
8. Minimize z - 8x1 + 6x2 + 11x3 subject to 5x1 x2 + 3x3 s 4 5x1 + x2 + 3x3 2 2 2x, + 4x2 + 7x3 s.5 2x1 + 4x2 + 7x3 2 3 X1 + X2 + X3 = 1 (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...
Use the simplex method to solve the linear programming problem. Maximize subject to z=900x4 + 800x2 + 400x3 X1 + x2 + x3 = 110 2X1 + 3x2 + 4x3 = 340 2xy + x2 + x3 180 X1 20, X220, X3 20. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The maximum is when x1 = ,x2 = , x3 = ,s2 = ,s2 =), and s3 =...