3. Consider the following parlor game to be played between two players. Each player begins with three chips: one red, one white, and one blue. Each chip can be used only

once. To begin, cach player selects one of her chips and places it on the table, concealed. Both players then uncover the chips and determine the payoff to the winning player. In particular, if both players play the same kind of chip, it is a draw; otherwise, the following table indicates the winner and how much she receives from the other player. Next, each player selects one of her two remaining chips and repeats the procedure, resulting in another payoff according to the following table. Finally, each player plays her one remaining chip, resulting in the third and final payoff. Winning Chip Payoff ($) Red beats white 25 White beats blue Blue beats red Matching colors 10 5 0 (a) Formulate the payoff matrix for the game and identify possible saddle points. [10 Marks] (b) Construct a linear programming model for each player in this game. [10 Marks] (c) Produce an appropriate code to solve the linear programming model for this game. [10 Marks] Identify the [10 Marks] (d) Solve the game for both players using the linear programming model. optimal solution and payoff, and interpret the corresponding strategies. [Hint: Each player has the same strategy set. A strategy must specify the first chip chosen, the second and third chips chosen. Denote the white, red and blue chips by W, R and B respectively. For example, a strategy "WRB" indicates first choosing the white and then choosing the red, before choosing blue at the end.]