A feasible region refers to the set of all possible solutions that satisfy a given set of constraints in optimization problems, particularly in linear programming.
In simpler terms, when you’re trying to make decisions under certain limitations—like budget, resources, or other criteria—the feasible region represents all the combinations of choices that you can work with without breaking any of those rules.
For example, imagine you want to buy fruits—say apples and bananas—within a budget of $10. If apples cost $2 each and bananas $1 each, the feasible region would depict all the combinations of apples and bananas you can purchase without exceeding your budget. This would be a graphical representation where the axes represent the quantities of apples and bananas, and the area that meets the budget constraint lines is the feasible region.
Identifying the feasible region is crucial in optimization, as it helps you find the best possible solution (or solutions) that remains within the acceptable limits.