6. A two-person zero-sum game is represented by the following pay-off matrix for player A.
| B plays 1 | B plays 2 | B plays 3 |
| A plays 1 | 5 | - 3 | 1 |
| A plays 2 | 2 | 5 | 0 |
| A plays 3 | - 4 | - 1 | 4 |
- Verify that there is no stable solution to this game.
- Formulate the game as a linear programming problem for player A. Define your variables clearly. Write the constraints as equations.
- Write down an initial simplex tableau, making your variables clear.