Optimization Question with Simplex Method

1. Determine the feasibility of each LP below by solving the Phase-1 LP: First, if an LP is not in standard form, convert it into standard form. Then, add artificial variables and define the Phase-1 LP; to reduce computation, you do not need to define artificial variables for equations that already isolate variables. For each LP determined as feasible, write down its feasible solution obtained from the last tableau of the Phase-1 LP, but you do not need to find its optimal solution. (a) max z = 2x1 + 3x2 - X4 s.t 2 1+ 2 + 213 II IV IA 16, 1+ 2 - 3 15, 1 +x3 - 24 -10, Ci 2 0 for all i (b) max s.t. - 201 - 23 + 24+ 25 = -2, - 23 - 34 + 26 - 8 = 4, + 23 - 0.5x4 + 207 = 1, 2 1+ 2 - 5x4 - 8 = 6, xi 2 0 for all