Solve the following LP problems. Z=2X1+12 Min St X, +X2 s 30 10x - 3X2 2...
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
Solve the problems: 1. x2 x33. 2. 2x, + 2x1 + 4x2-3x3 → min. 8x1 3x2 + 3x3 3 40, x2 20. 3. xi + X2 = 1, x120, x120.
Solve the problems: 1. x2 x33. 2. 2x, + 2x1 + 4x2-3x3 → min. 8x1 3x2 + 3x3 3 40, x2 20. 3. xi + X2 = 1, x120, x120.
1. Solve the following LP by the simplex method. Min z = 2x2 – Xı – X3 Subject to *1 + 2x2 + x3 = 12 2x1 + x2 – x3 = 6 -X1 + 3x2 = 9 X1, X2, X3 > 0
Consider the following LP z= 2x1-x2 st s r 22 0 1. Prove the feasible region of the above LP is convex set. (Note: You could not prove using graphical representation) (2 points) 2. Find extreme directions of the feasible region. (2 points)
Consider the following LP z= 2x1-x2 st s r 22 0 1. Prove the feasible region of the above LP is convex set. (Note: You could not prove using graphical representation) (2 points) 2. Find extreme directions...
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
Using the dual simplex, please solve the following linear program min z = x1 +x2 s.t. 2x tx2 5 2x1 + 3x2 26 (all x's are nonnegative)
Using the dual simplex, please solve the following linear program min z = x1 +x2 s.t. 2x tx2 5 2x1 + 3x2 26 (all x's are nonnegative)
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
1. Solve the following LP problem. Solve graphically. Maximize profit = 9x1+ 7x2 Subject to:2x1+ 1x2≤40 x1 + 3x2≤30 x1, x2≥0
Solve the following LP problem GRAPHICALLY Maximize profit = 9x1 + 7x2 Subject to: 2x1 + 1x2 ≤ 40 x1 + 3x2 ≤ 30 x1, x2 ≥ 0
2. Consider the following LP: Min z = -4x1 - 5x2 + 3x3 Subject to X1 + x2 + x3 = 10 X1 X2 > 1 X1 + 3x2 + x3 = 20 X1, X2, X3 20 (a) Solve the problem by Big M method. (b) Solve the problem by two-phase method.