$(15$ points$)$ Consider the following $LP.$

Maximize $4x_1+3x_2$

Subject $to{x}_1+2x_{2}10$

$2x_1+x_{2}8$

$x_1,x_{2}0$

Draw the feasible region $of$ the $LP(and$ lightly shade inside the feasible region$).$ Identify its

extreme points $on$ your drawing, and also determine the corresponding values for $x_1$ and $x_2$

$at$ these points. Provide the objective value $at$ each $of$ the extreme points. Based $on$ this, how

many optimal solutions are there? What are they? What $is$ the $LP\text{'}s$ optimal objective value?

$(15$ points$)$ Solve the $LP$ from problem $1$ using the $(dictionary)$ simplex method. Make sure

$to$ show your work. Observe how each dictionary corresponds $toan$ extreme point.