"Optimal solutions" are defined as feasible solutions where the objective functions reach their minimum or maximum values. For example, determining the "least cost" or "most profit" is a demonstration of an optimal solution. "Globally optimal solutions" exist when there are no better objective function values within other feasible solutions.
"Locally optimal solutions" exist when no other feasible solutions in the vicinity have better objective function values. This can be visualized as the bottom of a valley or top of a mountain peak, which is formed by the constraints or objective function. A feasible solution, which can be instantly known or difficult to find, is defined as a solution in which all constraints are satisfied.
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When the objective function is parallel to a binding constraint (i.e. constraint that is satisfied as an equation by the optimal solution), the objective function will assume the
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Either the most profitable or the least costly solution that simultaneously satisfies all the constraints of a Linear Programming (LP) problem. There are two important general properties
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