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In a linear programming problem, what is the difference between a feasible solution and an optimal solution?

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A feasible solution satisfies all the constraints of a linear programming problem, while an optimal solution is the feasible solution that results in the best value (maximum or minimum) of the objective function.

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Any solution that complies with all of the limitations imposed by the equality and inequality requirements is considered practical in the context of linear programming problems. While a feasible solution satisfies the requirements of the problem, it may not be the ideal one. On the other hand, an optimal solution is a particular workable solution that, depending on the problem's purpose, produces the most beneficial value for the objective function, which may be a maximum or minimum. Basically, an optimal solution is one that maximizes the goal function and remains feasible, whereas a feasible solution can exist anywhere within the specified restrictions.

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