Prepare a graph of the constraints and objective function and solve the following linear program problem: $(20$ points$).$

Maximize:

$f=2x_1-x_2$

Subject to

constraint $1$: $x_1+x_{2}2$

constraint $2$;$x_1+x_{2}5$

constraint $3$:$x_1-x_{2}1$

constraint $4$: $-x_1+x_{2}4$

constraint $5$: $x_{1}0$

constraint $6$: $x_{1}0$

Hints:

Draw the line of each constraint on the graph below $($two constraints are already drawn$)$

After drawing all the lines shade the optimal region.

Try $f=0,f=2$ and $f=4.$ Which one is the optimum, and what are the values of $x_1$ and $x_2?$