Please SHOW and EXPLAIN how you got the values inside of the payoff matrix.

Q2. The A.J. Swim team soon will have an important high school swim meet with the G.N. Swim Team. Each team has a star swimmer (John and Mark, respectively) who can swim very well in the 100-yard butterfly, backstroke, and breaststroke events. However, the rules prevent them from being used in more than two of these events. Therefore, their coaches now need to decide how to use them to maximum advantage. Each team will enter three swimmers per event (the maximum allowed). For each event, the following table gives the best time previously achieved by John and Mark as well as the best time for each of the other swimmers who will definitely enter that event. (Whichever event John or Mark does not swim, his team's third entry for that event will be slower than the two shown in the table). 1 The points awarded are 5 points for first place, 3 points for second place, 1 point for third place, and none for lower places. Both coaches believe that all swimmers will essentially equal their best times in this meet. Thus, John and Mark each will definitely be entered in two of these three events. The coaches must submit all their entries before the meet without knowing the entries for the other team, and no changes are permitted later. The outcome of the meet is very uncertain, so each additional point has equal value for the coaches. We now want to formulate this problem as a two-person, zero-sum game. The pure strategies for A.J Team are: 1) John does not swim butterfly; 2) John does not swim backstroke; 3) John does not swim breaststroke. The pure strategies for G.N. Team are: 1) Mark does not swim butterfly; 2) Mark does not swim backstroke; 3) Mark does not swim breaststroke. 1. (5 pts) Let the payoff entries be the total points earned in all three events by A.J. Team when a given pair of pure strategies are chosen by the teams. Write the payoff matrix and explain how you got the value associated with the combination of pure strategies (1,1). 2. (5 pts) Formulate problems for finding optimal mixed strategies for both teams according to the minimax criterion, i.e., write down the mathematical expressions of the optimization problem for each team. 3. (10 pts) Solve the formulated problem above using AMPL. What should the teams do according to the results by AMPL