Problem A: Consider the following LP problem to answer Questions 4 and 5. Maximise z =...
Question 2: Identify which of Cases (1)--(4) apply to the following LP problem. max z = 2x1 – X2 s. t. X1 – X2 < 1 2x1 + x2 > 6 X1, X2 > 0 (1) unbounded LP (2) infeasible LP (3) unique optimal solution (4) multiple optimal solutions
QUESTION 1 Given the following LP, answer questions 1-10 Minimize -3x15x2 Subject to: 3x2x 24 2x1+4x2 2 28 2s 6 x1, x2 20 How many extreme points exist in the feasible region for this problem? We cannot tell from the information that is provided The feasible e region is unbounded QUESTION 2 Given the following LP, answer questions 1-10 Minimize 2- 31+5x2 Subject to: 3x2x 24 2x1+4x2228 t is the optimal solution? (2, 6) (0, 12) (5,4.5) None of the...
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...
3. Use the two-phase simplex method to solve the following LP. Min z = x1 + 2x2 Subject to 3x1 + 4x2 < 12 2x1 - x2 2 2 X1, X2 20
Consider the following LP problem: Minimize Cost = 3x1 + 2x2 s.t. 1x1 + 2x2 ≤ 12 2x1 + 3 x2 = 12 2 x1 + x2 ≥ 8 x1≥ 0, x2 ≥ 0 A) What is the optimal solution of this LP? Give an explanation. (4,0) (2,3) (0,8) (0,4) (0,6) (3,2) (12,0) B)Which of the following statements are correct for a linear programming which is feasible and not unbounded? 1)All of the above. 2)Only extreme points may be optimal....
1. Use the Big M method to find the optimal solution to the following LP: Max z = 5x1 − x2 s.t.: 2x1 + x2 = 6 x1 + x2 ≤ 4 x1 + 2x2 ≤ 5 x1, x2 ≥ 0 Answer: z = 15, x1 = 3, x2 = 0.
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...
(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...
QUESTION 15 Describe the solution space for the following LP model: Maximize: 2x1 3x2 Subject to: 1: 2x1 3x2 2 18 2: 4x1 2x2 2 10 x1, x2 20 Multiple optimal solutions O Infeasible None of the above QUESTION 16 Describe the solution for the folowing LP model: Maximize: 2x1 3x2 Subject to: 1:4x1 +5x2 2 20 2: 3x1 2x2 212 x1, x2 20 A single optimal solution O Infeasible Multiple optimal solutions None of the above QUESTION 17 In...
Min Z = 6X1 + 4x2 Subject to Xi + 2x2 > 2 -X1 + 2x2 5 4 3x1 + 2x2 < 12 X1, X2 > 0