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Objective Function vs. Constraints in a Linear Programming Model

Under what circumstances is the objective function more important than the constraints in a linear programming model? Under what circumstances are the constraints more important than the objective function in a linear programming model?

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Objective more important than constraints

Generally optimization techniques have hard constraints, which mean that constraints put on the decision variables are absolute and cannot be violated. However, sometimes, we have a situation in mind for which hard constraints may not work and we may need more flexible or soft constraints. Such approach which is more flexible to constraints is called Goal Programming (GP) and involves both hard and soft constraints. In this approach we start with the statement of desired goals. But after some preliminary ...

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In this 350 word response with three references. The circumstances in which the objective function is more important than constraints is discussed. The opposite is also discussed..