Suppose we have the following LP model.Maximize Z = 10X + 5YSubject to:3X + 3Y ≤ 6 (Constraint 1)2X + 4Y ≥ 6 (Constraint 2)X, Y ≥ 0It came to be that the optimal solution is X = 1 and Y = 1. Which of the following options is a correct statement?Group of answer choicesConstraint 1 is a binding constraint, and constraint 2 is a non-binding constraint.Constraint 1 is a non-binding constraint, and constraint 2 is a binding constraint.Both constraints 1 and 2 are binding constraints.Both constraints 1 and 2 are non-binding constraints.
Question
Suppose we have the following LP model.Maximize Z = 10X + 5YSubject to:3X + 3Y ≤ 6 (Constraint 1)2X + 4Y ≥ 6 (Constraint 2)X, Y ≥ 0It came to be that the optimal solution is X = 1 and Y = 1. Which of the following options is a correct statement?Group of answer choicesConstraint 1 is a binding constraint, and constraint 2 is a non-binding constraint.Constraint 1 is a non-binding constraint, and constraint 2 is a binding constraint.Both constraints 1 and 2 are binding constraints.Both constraints 1 and 2 are non-binding constraints.
Solution
The correct statement is "Both constraints 1 and 2 are binding constraints."
Explanation:
A binding constraint is one that, if changed, would alter the optimal solution. In this case, if we substitute X = 1 and Y = 1 into the constraints, we get:
For Constraint 1: 31 + 31 = 6, which is equal to the right-hand side of the constraint.
For Constraint 2: 21 + 41 = 6, which is also equal to the right-hand side of the constraint.
Since both constraints are satisfied as equalities at the optimal solution, they are both binding constraints. If either constraint were changed, the optimal solution would also change. Therefore, the correct answer is "Both constraints 1 and 2 are binding constraints."
Similar Questions
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