Consider the following linear programming model:

Minimize objective function Z$3$X$1-3$X$2$

Subject to constraints:

X$1+3$X$2212$

X$1-$X$220$

X$126$

X$2$ $$10$

$5$X$1-5$X$260$

X$120$X$220$

a$)$ Trace the constraints and determine the region of feasible solutions $($DSA$).$ b$)$ The region of feasible solutions $($DSA$)$ has how many extreme points?

c$)$ Is the optimal solution unique?

d$)$ What are the extreme points that minimize the objective function Z$?$

e$)$ What is the value of $2$ at the optimum? Are there other optimal solutions?

NB: Draw the graph directly on your double examination sheet or on graph paper, choosing a suitable scale