Consider the following linear program: \begin{array}{l} \max x_{1}+x_{2} \\ \text { s.t.: } \\ \text { Cl } 3 x_{1}+2 x_{2} \leq 12 \\ \text { C2 } 2 x_{1}+3

x_{2} \leq 12 \\ \text { C3 } 2 x_{1}+2 x_{2} \leq 9 \\ \text { C4 } 2 x_{1}+2 x_{2} \geq 3 \\ \text { CS } \quad x_{1}, x_{2} \geq 0 \end{array} a) (5 points) Graph the feasible region of the LP. Is the feasible region unbounded? b) (35 points) Solve this problem using Simplex algorithm. Make sure to indicate: * Whether or not you need to perform Phase * Show the BV and NBV for each iteration of Simplex * Show the steps of the algorithm in the graph from point a) * Is this a unique or multiple solution?