Consider the following linear program with two decision variables,

$$

$1$

$$and

$$

$2$

$.$

max,

$$

$1$

$,$

$+$

$$

$2$

$,$

$$

$$

$.$

$$

$.$

$$

$,$

$3$

$$

$1$

$,$

$+$

$2$

$$

$2$

$,$

$<=$

$1$

$2$

$0$

$,$

$$

$1$

$,$

$+$

$2$

$$

$2$

$,$

$<=$

$6$

$0$

$,$

$$

$1$

$,$

$>=$

$1$

$5$

$,$

$$

$2$

$,$

$<=$

$2$

$5$

$,$

$$

$1$

$,$

$$

$2$

$,$

$>=$

$0$

Use the graphical solution method to determine the optimal solution and the associated objective function value