LP Problem

$\theta$ values and their corresponding number of iterations in brackets

Optimal Solution

Maximize $Z=6X_1+8X_2$

Subject to

$X_1+2X_2\le 12$

$X_1+X_2\le 10$

$X_1,X_2\ge 0$

0.1 $\to$ (79)

0.3 $\to$ (24)

0.5 $\to$ (12)

0.7 $\to$ (8)

0.9 $\to$ (6)

0.2 $\to$ (38)

0.4 $\to$ (17)

0.6 $\to$ (10)

0.8 $\to$ (7)

1.0 $\to$ (2)

$Z=64$

$X_1=8$

$X_2=2$

Maximize $Z=2X_1+3X_2$

Subject to

$X_1+X_2\ge 350$

$2X_1+X_2\le 600$

$X_1\ge 125$

$X_1{X}_2\ge 0$

0.1 $\to$ (92)

0.3 $\to$ (29)

0.5 $\to$ (17)

0.7 $\to$ (11)

0.9 $\to$ (8)

0.2 $\to$ (45)

0.4 $\to$ (21)

0.6 $\to$ (12)

0.8 $\to$ (10)

1.0 $\to$ (2)

$Z=1300$

$X_1=125$

$X_2=350$