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Objective function in Linear Programming

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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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All of the text below is from my knowledge and experience. Thus, no references have been provided. I am providing some references below for your knowledge.
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Constraints are not as important than the objective function. There are several cases where you have an objective function with no ...

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