1. (10 points = 1+1+1+2+1+2+2 points) Consider the Simplex method to solve the following linear programming problem (P). Give your answer to each question below with brief justification/explanation (no work, no points). (P) Maximize subject to 3x2+2x2 - 2x3 6x1 + x2 +3x3 s 18 01. 2.3 2 0. a. Write an equivalent problem that has an equality constraint by introducing a slack variable. b. How many and what nonbasic variables are in your formulation of (a)? c. What is the starting extreme point of the Simplex method (i.e., the values of variables)? a. From this starting point, what is the entering variable of the Simplex method? e. What is the leaving variable? f. After this pivot operation, what is the resulting point i.e. the values of variables)? g. Is the point of (1) optimal or not? (Don't forget to show your work.) 1. Write the dual problem of (P)