In a linear programming problem, the binding constraints for the optimal solution are 5X + 3Y...
Question:
In a linear programming problem, the binding constraints for the optimal solution are
5X + 3Y < 30
2X + 5Y < 20
a. Fill in the blanks in the following sentence: As long as the slope of the objective function stays between _____ and _____, the current optimal solution point will remain optimal.
b. Which of these objective functions will lead to the same optimal solution?
1) 2X + 1Y
2) 7X + 8Y
3) 80X + 60Y
4) 25X + 35Y
Binding and Non-Binding Constraint:
On solving a linear programming problem, we get an optimal solution in case the problem exhibits feasibility and boundedness of the constraints graphed. Once we get the optimal solution, we can figure out whether the constraint is binding or not. For each constraint, the binding factor can be identified.
So, if the optimal solution lies on the constraint, the constraint will be satisfied with an equality sign and that is when the constraint is said to be binding. In the other case, the constraint is said to be non-binding.
Answer and Explanation: 1
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View this answer(a.) We know that as long as the slope of the objective function lies between the slopes of the binding constraints, the current optimal solution...
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