Question 3 [20 points] Consider the linear program: max ( Ps.t. 2y1 + 7y2 3y3 + 4y4 3y1 2y2 + 4y4 5 y1 > 0, y2 > 0,43 > 0, y4 > 0. 1. Argue that (P) is infeasible. 2. Add slack/excess variables ys and ye to place the model in standard form. 3. Set up a phase-I model by introducing a single artificial variable a to the standard form model. 4. Starting with the basis composed of the artificial variable and an appropriate slack/excess variable, apply the simplex algorithm seen in class to the phase-I model to establish that (P) is infeasible. Among all eligible entering variables, always choose the one whose index is smallest. (When providing an answer to this problem, report (at least) the simpler tableau obtained at each iteration, and state what variables are entering/leaving the basis.)