Consider the Raw Material Acquisition case from week $1.$ The problem is formulated as a LP problem as follows:

Min Z $=20,000$X$1+15,000$X$2$

Subject to

$2$X$1+$ X$28$

$2$X$1+3$X$212$

X$1,$ X$20$

$$

Your Task

$1.$ Describe the feasible region.

$2.$ Select two levels of the objective function.

$3.$ What is the direction that improves the objective function value?

$4.$ Find the optimal solution and optimal value