Q$1.$ Solve the following problem, using the Corner Point Method.

Maximize profit $=30x_1+40x_2$

Subject to

$4x_1+2x_{2}16$

$2x_1-x_{2}2$

$x_{2}2$

$x_1,x_{2}0$

a$)$ Draw lines graphically and show the feasible region and comer points on your figure. $(10$ Points$)$

b$)$ Find the optimal value of decision variables and calculate profit at the optimal point. $(10$ Points$)$

c$)$ For the optimal solution, how much slack or surplus is there for each? $(5$ points$)$