8/17/2019 UNO-y-3

1/4

maxw=4y1+10y2

sa

3y1+6y2

8/17/2019 UNO-y-3

2/4

 !1/3"#1+ #2 #2 $ !1/3"#1+ #3 #3

cj 4 10 0 0 0

ci vb y1 y2 y3 y4 y5 ld

4 %1 1 0 1 2 0  1

10 %2 0 1 1/3 1 0  1/3

0 y5 0 0 1/3 )/3 1  1/3

WJ 4 10 *2/3 2 022/3

Cjwj 0 0 2/3 2 0

-. . --

(1 = 2/3

(2=2

(3=0

7= 22/3

Cj 0 0 0 0 1 1

Ci 8b x1 x2 x3 x4 1 2 ld 9

1 12 3 4 2 1 0 30

0 150

1 2: 1 1 5 0 1 30

0)5/2

;j10 4 5 ) 1 1 60

0

Cj;j 10 4 5 ) 0 0  

!1/:"#2  #2 $ !2"#2 + #1 #1

Cj 0 0 0 0 1 1

Ci 8b x1 x2 x3 x41

2 ld9

1 1 0 11/4 15/4 3/4 1

1/4225

600 x1 1 1/: 1/: 5/: 0 1/: )5/ 300

i&

;= 1 +2

sa2x1 + 3x2 + 4x3 + 2x4+ 1 = 300:x1 + x2 + x3 + 5x4 +

2= 300

max7= 4x1 + 2x2 + 3x3 +5x4

sa2x1 + 3x2 + 4x3 + 2x4= 300:x1 + x2 + x3 + 5x4 =300

8/17/2019 UNO-y-3

3/4

2

;j 0 11/4 15/4 3/4 1

1/4225

Cj;j 0

11/4

15/4

3/40 5/4

!4/15"#1 #1 $ !1/:"#1 + #2  #2

Cj 0 0 0 0 1 1

Ci 8b x1 x2 x3 x4 1 2 ld

0 x3 011/1

51 1/5 4/15

1/15

60

0 x1 1 1/30 0 3/5

1/302/15

30

;j 0 11/4 15/4 3/4 1 1/4 0

Cj;j 0

11/4

15/4

3/40 5/4

Cj 4 2 3 5

Ci 8b x1 x2 x3 x4 ld 93 x3 0 11/1

51 1/5

60300

4 x1 1 1/30 0 3/5 30 50;j 4 )/3 3 3  

Cj;j 0 1/3 0 2  

!5/3"#2

 #2 $ !1/5"#2 + #1

 #1

Cj 4 2 3 5

Ci 8b x1 x2 x3 x4 ld

3 x3 1/313/1

:1 0

50

5 x1 5/3 1/1: 0 1 50

;j 22/3 22/ 3 5 400

Cj;j 10/3 4/ 0 0  

Cj 0 0 0 1 0 1

Ci 8b x1 x2 x3 1 x4 2 ld 9

ax7= 4x1 + 2x2 + 3x3 +5x4

a11/15 x2 + x3 + 1/5x4=60(1 + 1/30 x2 + 3/5 x4 =30

i&

;= 1 +2

sa

x1 + x2 + 1= 10

2x1 x2 + x3 x4 + 1>= 10

i&

7= 3x1 + 2x2 + )x3

a

x1 + x2 = 10

2x1 x2 + x3 >= 10

8/17/2019 UNO-y-3

4/4

1 1 1 1 0 1 0 0 10

1 2 2 1 1 0 1 1 10 5

;j 1 0 1 1 1 1 20

Cj;j 1 0 1 0 1 0

#2  #2 $ #2 + #1  #1

Cj 0 0 0 1 0 1

Ci 8b x1 x2 x3 1 x4 2 ld 9

1 1 0 1/2 1/2 1

1/21/2 15

30

0 (1 1

1/21/2 0

1/2

 1/2

5

;j 0 1/2 1/2 1

1/21/2 15

Cj;j 0

1/2

1/20 1/2 1/2

#2  #2 $ #2 + #1  #1

Cj 0 0 0 1 0 1

Ci 8b x1 x2 x3 1 x4 2 ld

0 (2 0 1 1 2 1 1 30

0 (1 1 0 1 1 1 1 20

;j 0 0 0 0 0 0 0

Cj;j 0 0 0 1 0 1

Cj 3 2 ) 0

Ci 8b x1 x2 x3 x4 .d

2 (2 0 1 1 1 30

3 x1 1 0 1 1 20

;j 3 2 5 5  

Cj;j 0 0 2 5  

i&

7= 3x1 + 2x2 + )x3

a

x2 + x3 x4 = 30X1 – ½ x2 + ½ x3 – ½ x4 = 20