Consider the mathematical program max 3x1 x2 +3x3 s.t. 2X1 + X2 + X3 +X4-2 x1...
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...
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
Consider the following LP problem max z = x1 +2x2 + x3 + x4 s.t. x1 + 2x2 + x3 く2 +2x3 く! X1, x2, x3, x4 20 a) Obtain the dual formulation of the LP.
Consider the following LP: Max x1 +x2 +x3 s.t. x1 +2x2 +2x3 ≤ 20 Solve this problem without using the simplex algorithm, but using the fact that an optimal solution to LP exists at one of the basic feasible solutions.
(1) Convert the following LPs to standard form: 22 (a) max z 3x1 + 2x2 s.t. 21 < 40 X1 + x2 < 80 2x1 + x2 < 100 X1, X2 > 0 (b) max z = 2x1 s.t. X1 – X2 <1 2x1 + x2 > 6 X1, X2 > 0 (c) max z = 3x1 + x2 s.t. 1 > 3 X1 + x2 < 4 2x1 – X2 = 3 X1, X2 > 0
2x1 − x2 − 3x3 − 2x4 = 1 x1 − x2 − 4x3 − 2x4 = 5 3x1 − x2 − x3 − 3x4 = −2 x1 + 2x3 − x4 = −4
Min 2x1 + x2 s.t. x1 + x2 ≥ 4 x1 – x2 ≥ 2 x1 – 2x2 ≥ –1 x1 ≥ 0, x2 ≥ 0 Please solve the linear program graphically, showing the objective function, all constraints, the feasible region and marking all basic solutions (distinguishing the ones that are feasible).
samplex Problem1: Solve the following problem using simplex method: Max. z = 2 x1 + x2 – 3x3 + 5x4 S.t. X; + 7x2 + 3x3 + 7x, 46 (1) 3x1 - x2 + x3 + 2x, 38 .(2) 2xy + 3x2 - x3 + x4 S 10 (3) E. Non-neg. x > 0, x2 > 0, X3 > 0,44 20 Problem2: Solve the following problem using big M method: Max. Z = 2x1 + x2 + 3x3 s.t. *+...
Max: 70X1 + 40X2 Constraints: X1 + X2 < 700 X1 – X2 < 300 2X1 + X2 < 900 3X1 + 4X2 < 2400 X1, X2 > 0 Solve using either the level curve or enumeration approach. Please show all of the intersection points, feasible region, and the optimal solution.
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....