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2) (25pts) For the LP below: mìn x,-2x2-3x3 +2xa x, +2x,-,+3x, +x,-12 etermine the optimal soluti...
6, Maximize z = 2x1 + x2 + 3x3 subject to x 3x2 5x3 s 10 2x x 20, x, 0, x320. (a) State the dua...
6, Maximize z = 2x1 + x2 + 3x3 subject to x 3x2 5x3 s 10 2x x 20, x, 0, x320. (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.
6, Maximize z = 2x1 + x2 + 3x3 subject to x 3x2 5x3 s...
SOLVE STEP BY STEP! 4. Consider the following LP: Minimize z = x; +3x2 - X3...
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...
Problem 1 (20 pts) Consider the mathematical program max 3x1+x2 +3x3 s.t. 2x1 +x2 + x3 +x2 x1 + 2x2 + 3x3 +2xs 5 2x 2x2 +x3 +3x6-6 Xy X2, X3, X4, Xs, X620 Three feasible solutions ((a) through (c...
Problem 1 (20 pts) Consider the mathematical program max 3x1+x2 +3x3 s.t. 2x1 +x2 + x3 +x2 x1 + 2x2 + 3x3 +2xs 5 2x 2x2 +x3 +3x6-6 Xy X2, X3, X4, Xs, X620 Three feasible solutions ((a) through (c)) are listed below. (0.3, 0.1, 0.4, 0.9, 1.65, 1.6) (c) x Please choose one appropriate interior point from the list, and use the Karmarkar's Method at the interior point and determine the optimal solution. 25
Problem 1 (20 pts) Consider...
Probs. 3-4-5 refer to the following problem and its complete solution Max . Z 4x1 + 6x2 + 3x3 + x+ ?2x1 + 2x2...
Probs. 3-4-5 refer to the following problem and its complete solution Max . Z 4x1 + 6x2 + 3x3 + x+ ?2x1 + 2x2 + 4x3 + 3x+ 550 (x5) 2x1 + 3x2 + x3 + 2x‘ S 20O (x7) R.S 4-6 -31 /4 3 1 550 700 200 0 o1 3 o 2 Z O 400 2/11 1/12/10 o 1/11 662 / ง 9 525 2 /20 425 2/ 25 1/2-1/10 13/20 1 0 。 3a. Read off the...
z= 4x Max 6*2 3x3 (x,) () (x,) 3x 550 2x2 2x 4x3 + + +...
z= 4x Max 6*2 3x3 (x,) () (x,) 3x 550 2x2 2x 4x3 + + + 1 x 700 + 4x + 2 2x 200 3x2 + + 3 2x x. + R.S. 6 Eq.# 2 2 B.V. C -1 -3 -6 4 1 550 C O 1 3 2 /2 1 700 1 1 2 4 2 200 1 2 1 3 2 O 3 400 2 C O -1 1 4162/3 2/3 5/3 O 1 1 4/s O...
6, Maximize z = 2x1 + x2 + 3x3 subject to x 3x2 5x3 s 10 2x x 20, x, 0, x320. (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.
6, Maximize z = 2x1 + x2 + 3x3 subject to x 3x2 5x3 s...
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...
Problem 1 (20 pts) Consider the mathematical program max 3x1+x2 +3x3 s.t. 2x1 +x2 + x3 +x2 x1 + 2x2 + 3x3 +2xs 5 2x 2x2 +x3 +3x6-6 Xy X2, X3, X4, Xs, X620 Three feasible solutions ((a) through (c)) are listed below. (0.3, 0.1, 0.4, 0.9, 1.65, 1.6) (c) x Please choose one appropriate interior point from the list, and use the Karmarkar's Method at the interior point and determine the optimal solution. 25
Problem 1 (20 pts) Consider...
Probs. 3-4-5 refer to the following problem and its complete solution Max . Z 4x1 + 6x2 + 3x3 + x+ ?2x1 + 2x2 + 4x3 + 3x+ 550 (x5) 2x1 + 3x2 + x3 + 2x‘ S 20O (x7) R.S 4-6 -31 /4 3 1 550 700 200 0 o1 3 o 2 Z O 400 2/11 1/12/10 o 1/11 662 / ง 9 525 2 /20 425 2/ 25 1/2-1/10 13/20 1 0 。 3a. Read off the...
z= 4x Max 6*2 3x3 (x,) () (x,) 3x 550 2x2 2x 4x3 + + + 1 x 700 + 4x + 2 2x 200 3x2 + + 3 2x x. + R.S. 6 Eq.# 2 2 B.V. C -1 -3 -6 4 1 550 C O 1 3 2 /2 1 700 1 1 2 4 2 200 1 2 1 3 2 O 3 400 2 C O -1 1 4162/3 2/3 5/3 O 1 1 4/s O...
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