What does the final tableau indicate about the basic solution and optimal value in linear programming?

The final tableau indicates that the basic solution consists of the values of the basic variables, while the optimal value is found in the check column of the tableau. If there are no negative entries in the index row, the solution is optimal, and the corresponding value in the b column represents the optimal value of the objective function.

In linear programming, the final tableau reveals the basic solution through the values of the basic variables listed in the b column. When the index row contains no negative entries, it signifies that the optimal solution has been reached. The optimal value of the objective function is then given by the corresponding entry in the b column, confirming the maximum or minimum value of the function under the given constraints.