min -x1 - x2

subject to: x1 + x2 <= 2

2x1 + 3x2 <=12

3x1 + x2 <=12

x1, x2 >=0

a) Use the Simplex Method to solve the linear program in Problem 4. (Like in Problem 4, use the slack variables as the initial basic variables to start.) At each step, please state clearly what the basis matrix, the entering variable, the exiting variable are, or how you judge the current solution is optimal. At the end, please clearly state the optimal solution and the optimal objective value.

b) Using the graph in Problem 4, Part a), provide the sequence of the extreme points (or Basic Feasible Solution) that were visited by the Simplex method. For each  extreme point, please indicate their associated basic variables and non-basic variables