Consider the two-player zero-sum game with payoff matrix

$$A=\left(\begin{array}{rrr} 2 & 0 & -2 \\ 3 & 4 & 5 \\ 6 & 0 & 6 \end{array}\right)$$

Express the problem of finding the column player's optimal strategy as a linear programming problem in which $x_{1}+x_{2}+x_{3}$ is to be maximized subject to some constraints.

Solve this problem using the simplex algorithm and find the optimal strategy for the column player.

Find also, from the final tableau you obtain, both the value of the game and the row player's optimal strategy.