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Consider the following 2-person zero-sum games' payoff matrix. Do they have an optimal pure strategy pair? If yes, identify the optimal pure strategies for each of the players, and if not, present the optimal mixed strategies by solving the LP model.
V=[1 2 4 9 5 1]
Options: Player I: x1=0.67; x2=0.33; v=3 Player II: y1=0.5; y2=0.5; y3=0; v=3
Player I: x1=0.67; x2=0.33; v=3 Player II: y1=0.0; y2=0.5; y3=0.5; v=3
Player I: x1=0.67; x2=0.33; v=1 Player II: y1=0.0; y2=0.5; y3=0.5; v=1
Player I: x1=0.67; x2=0.33; v=1 Player II: y1=0.2; y2=0.3; y3=0.5; v=1
Player I: x1=0.5; x2=0.5; v=3 Player II: y1=0.0; y2=0.5; y3=0.5; v=3
Player I: x1=0.33; x2=0.67; v=1 Player II: y1=0.0; y2=0.5; y3=0.5; v=1