dual simplex method

The dual simplex method is an optimization technique used in linear programming, which focuses on improving problems where some constraints are not satisfied. Instead of maximizing or minimizing an objective function directly, it works on an alternate version of the problem, maintaining feasibility while seeking optimal solutions. This method updates the solution by pivoting on constraint violations, ensuring that all adjustments lead to valid outputs. It's particularly useful in situations like resource allocation, where constraints change frequently but maintaining a feasible solution is critical. Overall, it helps find the best solution while respecting necessary limitations.