
Solve the system X1 + 2x2 - 3x3 = 5 2x1 + x2 – 3x3 = = 13 - X1 + X2 = -8 O a. x= 1, SEC 0 Ob. tec x=1 1 Ос. 2 x= 3, SEC -5 0 d. 1 x=0 -1 gree -1 SEC x=s -1 0 Of. 1 X=S 0 -1 SEC 0
Solve the system X1 + 2x2 – 3x3 = 5 2x1 + x2 – 3x3 = 13 - X1 + X2 = -8 1 x= 1), sec 0 a. b. N x=s3 sec -5 0 X=S SEC -1 O O d. X=t 1 1 1 tec Oe. x= -1, sec 0
Solve the system
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Solve the system X1 + 2x2 – 3x3 = 5 2x1 + x2 – 3x3 = 13 - X1 + X2 -8 2 X=S 3 SEC -5 a. b. 1 x=t0], tec x=s -1 SEC d. 1 x= t 1 tec 1 e. O 1 0 X=S SEC -1 0 o f. 1 SEC x=s 1 0
Solve the given system of equations using either Gaussian or Gauss-Jordan elimination x1 + 2x2-3x3 = 19 2x1 -X2+ X3 - 4X1- x2 + x3= 8
3. Solve the following system of homogeneous equations 2.x1 + x2 + 3x3 = 0 x₂ + 2x2 x2 + x3
1. Find all solutions to the system x1 + 2x2 + 3x3 = 8 1 x1 - x2 + 3x3 = 5 =>{801_ ) but ke 2. Is a basis for R3? 13 12
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...
Consider the mathematical program max 3x1 x2 +3x3 s.t. 2X1 + X2 + X3 +X4-2 x1 + 2x2 + 3x3 + 2xs 5 2x1 + 2x2 + x3 + 3x6 = 6 Three feasible solutions ((a) through (c)) are listed below. (b) xo) (0.9, 0, 0, 0.2,2.05, 1.4) (c) xo) (0.3, 0.1, 0.4, 0.9, 1.65, 1.6) Please choose one appropriate interior point from the list, and use the Karmarkar's Method at the interior point and determine the optimal solution.
2x1 − x2 − 3x3 − 2x4 = 1 x1 − x2 − 4x3 − 2x4 = 5 3x1 − x2 − x3 − 3x4 = −2 x1 + 2x3 − x4 = −4
Problem 5: a) (2 Points) Using the two-phase simplex procedure solve Minimize 3X1 + X2 + 3X3-X4 Subject to 1 2.x2 - ^3 r4 0 2x1-2x2 + 3x3 + 3x4 9 T1, x2, x3, x4 2 0. b) (2 Points) Using the two-phase simplex procedure solve Minimize Subject to x1+6x2-7x3+x4+5x5 5x1-4x2 + 132:3-2X4 + X5-20 X5 〉 0.