1. Use the Simplex algorithm to solve the following LP models: а. max z = 2x1 – x2 + x3 s.t. 3x1 + x2 + x3 < 60 2x1 + x2 + 2x3 < 20 2x1 + 2x2 + x3 < 20 X1, X2, X3 2 0 b. min z = - 3x1 + 8x2 4x1 + 2x2 < 12 2х + 3x2 S 6 s.t. X1, x2 2 0)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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1. Use the Simplex algorithm to solve the following LP models:
а.
max z = 2x1 – x2 + x3
s.t.
3x1 + x2 + x3 < 60
2x1 + x2 + 2x3 < 20
2x1 + 2x2 + x3 < 20
X1, X2, X3 2 0
b.
min z = -3x, + 8x2
s.t.
4.x1 + 2x2 < 12
2x1 + 3x2 < 6
X1, X2 2 0)
2. Solve the following LP models with both Big M and Two Phase Simplex
Algorithms:
а.
min z = 4x1 + 4x2 + x3
X1 + x2 + x3<2
2x1 + x2
s.t.
<3
2x1 + x2 + 3x3 2 3
X1, X2, Xz 2 ()
b.
min z
3x1
s.t.
2x1 + x2 > 6
3x1 + 2x2 = 4
X1, X2 2 0
Transcribed Image Text:1. Use the Simplex algorithm to solve the following LP models: а. max z = 2x1 – x2 + x3 s.t. 3x1 + x2 + x3 < 60 2x1 + x2 + 2x3 < 20 2x1 + 2x2 + x3 < 20 X1, X2, X3 2 0 b. min z = -3x, + 8x2 s.t. 4.x1 + 2x2 < 12 2x1 + 3x2 < 6 X1, X2 2 0) 2. Solve the following LP models with both Big M and Two Phase Simplex Algorithms: а. min z = 4x1 + 4x2 + x3 X1 + x2 + x3<2 2x1 + x2 s.t. <3 2x1 + x2 + 3x3 2 3 X1, X2, Xz 2 () b. min z 3x1 s.t. 2x1 + x2 > 6 3x1 + 2x2 = 4 X1, X2 2 0
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