6. The payoff matrix for player \(A\) in a two-person zero-sum game is shown below.
| \cline { 3 - 5 }
\multicolumn{2}{c|}{} | \(B\) |
| \cline { 3 - 5 }
\multicolumn{2}{c|}{} | I | II | III |
| \multirow{2}{*}{\(A\)} | I | - 2 | 3 | - 1 |
| \cline { 2 - 5 } | II | 4 | - 5 | 2 |
- Formulate this information as a linear programming problem, the solution to which will give the optimal strategy for player \(B\).
(7 marks) - By solving this linear programming problem, find the optimal strategy for player \(B\) and the value of the game.