Which of the following describes a mutually exclusive constraint?

Which of the following describes a mutually exclusive constraint?

• A. Sum of binary variables must equal 1.
• B. Sum of binary variables ≤ 1.
• C. All variables can be 1.
• D. Sum of all variables must equal total capacity.

Answer: (B)

The correct choice regarding a mutually exclusive constraint is that the sum of binary variables must equal 1. This means that among the binary variables involved in the constraint, only one can take the value of 1 (true), while the others must be 0 (false). This is a common way to enforce mutually exclusive conditions in linear programming models, where exactly one option must be chosen from a set of alternatives. The other answers illustrate different scenarios that do not create a mutually exclusive condition. For instance, saying the sum of binary variables is less than or equal to 1 allows for the possibility of none being selected, or only one, which does not strictly enforce mutual exclusivity. Similarly, stating that all variables can be 1 contradicts the principle of mutual exclusivity, as multiple selections would be allowed. Finally, saying that the sum of all variables must equal total capacity does not necessarily imply that the choices are mutually exclusive; it is more about adhering to a capacity limit without defining how selection among variables takes place.

The correct choice regarding a mutually exclusive constraint is that the sum of binary variables must equal 1. This means that among the binary variables involved in the constraint, only one can take the value of 1 (true), while the others must be 0 (false). This is a common way to enforce mutually exclusive conditions in linear programming models, where exactly one option must be chosen from a set of alternatives.

The other answers illustrate different scenarios that do not create a mutually exclusive condition. For instance, saying the sum of binary variables is less than or equal to 1 allows for the possibility of none being selected, or only one, which does not strictly enforce mutual exclusivity. Similarly, stating that all variables can be 1 contradicts the principle of mutual exclusivity, as multiple selections would be allowed. Finally, saying that the sum of all variables must equal total capacity does not necessarily imply that the choices are mutually exclusive; it is more about adhering to a capacity limit without defining how selection among variables takes place.