Question $2.$

a$.$

Determine whether the following linear programming problem is feasible or not. If feasible, solve the problem graphically; if not, explain why it is not feasible.

minimize $z=-3x_1$

subject $to$

$2x_1+x_{2}3$

$3x_1-x_{2}2$

$x_{2}2$

$x_1,x_{2}0$

b$.$

Solve the following linear programming problem graphically.

minimize $z=-3x_1$

subject $to$

$2x_1+x_{2}3$

$3x_1-x_{2}2$

$x_1+x_{2}1$