Soft Constraints in Linear Programming
In linear programming, we usually consider constraints like "the barge must be turned over in 2.5 hours ". However, looking for considerably better solutions (e.g., with a revenue of 30,000 instead of 20,000) at a slightly higher turnover time often makes sense. Then, we do not model the turnover time as a "hard" constraint but penalize exceeding it. This concept is called a "soft constraint".
This video contains two questions: explaining changes in the slope of the objective function for increasing turnover times and modeling the problem with a soft constraint on coal availability.
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