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Punto 1

The document presents a linear programming problem with the objective to maximize z=5x1+9x2+7x3 subject to the given constraints. It provides the standard form of the problem and solves it using the simplex method, arriving at the optimal solution x1=0, x2=1, x3=0, with maximum z=0.

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Cardenas Katherinne
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66 views4 pages

Punto 1

The document presents a linear programming problem with the objective to maximize z=5x1+9x2+7x3 subject to the given constraints. It provides the standard form of the problem and solves it using the simplex method, arriving at the optimal solution x1=0, x2=1, x3=0, with maximum z=0.

Uploaded by

Cardenas Katherinne
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as XLSX, PDF, TXT or read online on Scribd
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max z 5x1+9x2+7x3

s.a. restricciones BASICA Z X1 X2


x1+3x2+2x3<= 10 Z 1 -5 -9
3x1+4x2+2x3<= 12 s1 0 1 3
2x1+x2+2x3<= 8 s2 0 3 4
x1,x2,x3>= 0 s3 0 2 1

Forma estandar
BASICA Z X1 X2
Z-5x1-9x2-7x3+0s1+0s2+0s3 Z 1 -5 -9
s1 0 1 3
x1+3x2+2x3+s1= 10 x2 0 0.75 1
3x1+4x2+2x3+s2= 12 s3 0 2 1
2x1+x2+2x3+s3= 8
x1,x2,x3,s1,s2,s3>= 0 x2*9 0 6.75 9
x2*-3 0 -2.25 -3
x2*-1 0 -0.75 -1

BASICA Z X1 X2
Z 1 1.75 0
s1 0 -1.25 0
x2 0 0.75 1
s3 0 1.25 0

BASICA Z X1 X2
Z 1 1.75 0
x1 0 -2.5 0
x2 0 0.75 1
s3 0 1.25 0

x1*2,5 0 -6.25 0
x1*-0,5 0 1.25 0
x1*-1,5 0 3.75 0

BASICA Z X1 X2
Z 1 -4.5 0
x1 0 -2.5 0
x2 0 2 1
s3 0 5 0

BASICA Z X1 X2
Z 1 -4.5 0
x1 0 -2.5 0
x2 0 2 1
x3 0 1 0

x3*4,5 0 4.5 0
x3*2,5 0 2.5 0
x3*-2 0 -2 0

BASICA Z X1 X2
Z 1 0 0
x1 0 0 0
x2 0 0 1
x3 0 1 0
X3 X4 X5 X6 SOLUCIÓN
-7 0 0 0 0
2 1 0 0 10 3.33333333
2 0 1 0 12 3
2 0 0 1 8 8

X3 X4 X5 X6 SOLUCIÓN
-7 0 0 0 0
2 1 0 0 10
0.5 0 0.25 0 3
2 0 0 1 8

4.5 0 2.25 0 27
-1.5 0 -0.75 0 -9
-0.5 0 -0.25 0 -3

X3 X4 X5 X6 SOLUCIÓN
-2.5 0 2.25 0 27 -10.8
0.5 1 -0.75 0 1 2
0.5 0 0.25 0 3 6
1.5 0 -0.25 1 5 3.33333333

X3 X4 X5 X6 SOLUCIÓN
-2.5 0 2.25 0 27
1 2 -1.5 0 2
0.5 0 0.25 0 3
1.5 0 -0.25 1 5

2.5 5 -3.75 0 5
-0.5 -1 0.75 0 -1
-1.5 -3 2.25 0 -3

X3 X4 X5 X6 SOLUCIÓN
0 5 -1.5 0 32 -7.11111111
1 2 -1.5 0 2 -0.8
0 -1 1 0 2 1
0 -3 2 1 2 0.4

X3 X4 X5 X6 SOLUCIÓN
0 5 -1.5 0 32
1 2 -1.5 0 2
0 -1 1 0 2
0 -0.6 0.4 0.2 0.4

0 -2.7 1.8 0.9 1.8


0 -1.5 1 0.5 1
0 1.2 -0.8 -0.4 -0.8

X3 X4 X5 X6 SOLUCIÓN
0 2.3 0.3 0.9 33.8
1 0.5 -0.5 0.5 3
0 0.2 0.2 -0.4 1.2
0 -0.6 0.4 0.2 0.4

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