Problem 2 (20 pts): Consider the linear program below. Please use simplex tableau to completely solve it. For each step, draw the simplex tableau. Clearly mark what is the current basis, the current basic solution, and the corresponding objective function value. You can firstly find a trivial BFS and start from it. Also, compare the BFS and the second tableau obtained in this question. They should be consistent.
Maximize T1 + 212T2 + 313T3 + 814T4
subject to:
I1T2 + 83T3 < 2T1 + 13T4
%4 < 1T2 + 282T3 + 3T4 + 4T4 < 8
T1, T2, T3, T4 > 0