A linear programming model is given as follows:

Minimize $Z=8x_1+6x_2$

Subject $to$

$4x_1+2x_{2}20$

$-6x_1+4x_{2}12$

$x_1+x_{2}6$

$x_1,x_{2}0$

$($a$)$ Define the feasible solution area and obtain the optimal solution graphically

$($b$)$ If the coefficient of $x_2$ in the objective function decreases to $4,$ what effect will be$?$

$($c$)$ If the second constraint, $-6x_1+4x_{2}12,$ is removed from the given model, what effect will be$?$

$($d$)$ If a new constraint, $4x_1+6x_{2}24,$ is added to the given model, what effect will be$?$