$(20$pts$)$ maxz$=1000x_1+2000x_2$

$s.t.x_1+x_{2}500$

$x_{1}200$

$2x_1+5x_{2}1200$

$x_1,x_{2}0$

For the given LP:

a$)$ Plot the constraints and determine the feasible region clearly.$(5$ pts$.)$

b$)$ Solve by using graphical method. $(5$ pts$.)$

c$)$ Which constraints are binding and non$-$binding? $(5$ pts$.)$