3(45pts) Consider the two-player Rock-Paper-Scissors game with the following payoff table for Player 1: Player 2 Strategy R P S Player 1 R 0 -1 1 P S 1 1 0 1 -1 0 (a) Set up a linear programming problem for Player 1's optimal strategy. (b) The linear programming problem for Player 2's optimal strategy is to minimize z = 1/4 subject to: V1+2y3 y4, 211 + 1/2 S V4, 2y2 + y3 y4, and y1 + 2 + y31 with y, 20 with i=1,2,3,4 with the game value v=y4-1. Use the Big M method to set up an artificial linear programming problem for Player 2's mixed strategy (31, 32, 33). (c) Use the simplex tableaux to find the first two basic-feasible (BF) solutions only for the artificial Big M problem above.