Minimize $Z=3X_1+2X_2$

Subject to

$5X_1+X_2\ge 10$

$X_1+X_2\ge 6X_1+4X_2\ge 12$

$X_1{X}_2\ge 0$

0.1 $\to$ (90)

0.3 $\to$ (27)

0.5 $\to$ (15)

0.7 $\to$ (10)

0.9 $\to$ (7)

0.2 $\to$ (43)

0.4 $\to$ (20)

0.6 $\to$ (11)

0.8 $\to$ (9)

1.0 $\to$ (2)

$Z=13$

$X_1=1$

$X_2=5$

Minimize $Z=20X_1+10X_2$

Subject to

$X_1+2X_2\le 40$

$3X_1+X_2\ge 30$

$4X_1+3X_2\ge 60$

$X_1{X}_2\ge 0$

0.1 $\to$ (90)

0.3 $\to$ (27)

0.5 $\to$ (15)

0.7 $\to$ (10)

0.9 $\to$ (7)

0.2 $\to$ (43)

0.4 $\to$ (20)

0.6 $\to$ (11)

0.8 $\to$ (9)

1.0 $\to$ (2)

$Z=240$

$X_1=6$

$X_2=12$

Maximize $Z=16X_1+17X_2+10X_3$

Subject to

$X_1+X_2+4X_3\le 2000$

$2X_1+X_2+X_3\le 3600$

$X_1+2X_2+2X_3\le 2400$

$X_1\le 30$

$X_1,X_2,X_3\ge 0$

0.1 $\to$ (122)

0.3 $\to$ (37)

0.5 $\to$ (19)

0.7 $\to$ (12)

0.9 $\to$ (10)

0.2 $\to$ (58)

0.4 $\to$ (26)

0.6 $\to$ (15)

0.8 $\to$ (11)

1.0 $\to$ (3)

$Z=20625$

$X_1=30$

$X_2=1185$

$X_3=0$