Consider the following LP z= 2x1-x2 st s r 22 0 1. Prove the feasible region of the above LP is c...
Solve the following LP problems. Z=2X1+12 Min St X, +X2 s 30 10x - 3X2 2 1
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...
(1) r md le atletne po nts or the region denned by these inequalities (ii) Does this set have any direction of unboundedness? Either prove that non of a direction of unboundedness. 5. Consider the linear program minimize z=-5x1-7T2 subject to -3 +2r2 S 30 ,222 0 (i) Draw a graph of the feasible region (i) Determine the extreme points of the feasible region (ii) Determine two linearly independent eztreme directions of unboundedness (iv) Convert the linear program to standard...
Find the duals of the following LP.
(a) Max Z--2x1 + x2 - 4xz + 3x4 st. x1 + x2 + 3x2 + 2x4 S4 X1 -X3 + X, 2-1 2x1 + x2 32 X1 + 2x2 + x3 + 2x4 = 2 X2, X3, X, 20 (b) Min Z=0.4x1 +0.5x2 st. 0.3x2 +0.1x, 32.7 0.5x7 +0.5x2 = 6 0.6x, +0.4x, 26 X1, X220
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...
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. Consider the following LP: Max z 5x1 X2 st. 2x1 xS6 6x1X2S 12 Plot the constraints on the graph and identify the feasible region and determine the optimal value of the objective function and the values of the decision variables. 2. Priceler manufactures sedans and wagons. The number of vehides that can be sold each of the next three months are listed to Table 1. Each sedan sells for $10000 and each wagon sells for $11000. It cost $7000...
Q4. (Sensitivity Analysis: Adding a new constraint) (3 marks) Consider the following LP max z= 6x1+x2 s.t.xi + x2 S5 2x1 + x2 s6 with the following final optimal Simplex tableau basis x1 r2 S2 rhs 0 0 18 0.5 0.5 0.5 0.5 x1 where sı and s2 are the slack variables in the first and second constraints, respectively (a) Please find the optimal solution if we add the new constraint 3x1 + x2 S 10 into the LP (b)...
Q3. (Dual Simplex Method) (2 marks) Use the dual Simplex method to solve the following LP model: max z= 2x1 +4x2 +9x3 x1 x2 x3 S 1 -x1+ X2 +2x3 S -4 x2+ X1,X2,X3 S 0
Q3. (Dual Simplex Method) (2 marks) Use the dual Simplex method to solve the following LP model: max z= 2x1 +4x2 +9x3 x1 x2 x3 S 1 -x1+ X2 +2x3 S -4 x2+ X1,X2,X3 S 0
Consider the following Linear Problem Minimize 2x1 + 2x2 equation (1) subject to: x1 + x2 >= 6 equation (2) x1 - 2x2 >= -18 equation (3) x1>= 0 equation (4) x2 >= 0 equation (5) 13. What is the feasible region for Constraint number 1, Please consider the Non-negativity constraints. 14. What is the feasible region for Constraint number 2, Please consider the Non-negativity constraints. 15. Illustrate (draw) contraint 1 and 2 in a same graph and find interception...