Consider the following linear program:

Maximize $Z=,3x+9y$

Subject $to$:

$,x+3y60$

$,x+y,10$

$,x-y0$

$,x0,y0$

a$)$ Graph the feasible region and identify all corner point feasible solutions. $(10$

points$)$

b$)$ Identify the optimal solution and the optimal objective function value. $(10$ points$)$

c$)$ Provide the adjacent corner point feasible solutions to $(0,10).(10$ points$)$