Assuming W1, W2, and W3 are 0-1 integer variables, we have a constraint W1 + W2 + W3 ≤ 2 in the model. Which of the following statements is correct?Group of answer choicesminimum two variables can occur at the same time.all variables can be 0 at the same time.the variables are mutually exclusive.none of the above.
Question
Assuming W1, W2, and W3 are 0-1 integer variables, we have a constraint W1 + W2 + W3 ≤ 2 in the model. Which of the following statements is correct?Group of answer choicesminimum two variables can occur at the same time.all variables can be 0 at the same time.the variables are mutually exclusive.none of the above.
Solution
The correct statement is "all variables can be 0 at the same time."
Explanation: The constraint W1 + W2 + W3 ≤ 2 means that the sum of the variables W1, W2, and W3 cannot exceed 2. This does not prevent all variables from being 0 at the same time. In fact, if all variables are 0, the constraint is satisfied because 0 + 0 + 0 = 0, which is less than 2.
The statement "minimum two variables can occur at the same time" is not necessarily correct because it's possible for only one variable to be 1 and the others to be 0, which would still satisfy the constraint.
The statement "the variables are mutually exclusive" is also not correct because it's possible for more than one variable to be 1 at the same time, as long as the sum does not exceed 2.
Therefore, the correct answer is "all variables can be 0 at the same time."
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