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?

Question

BlackTom AI · Accepted Answer

Consider the constraint W1 + W2 + W3 ≤ 2 with W1, W2, W3 ∈ {0,1}.

Option 1: 'minimum two variables can occur at the same time.' This would require a feasible assignment with at least two of W1, W2, W3 equal to 1. While it is true that two variables can be 1 (for example 1,1,0), the statement asserts that the minimum number of ones is two in all feasible solutions. However, the all-zero combination (0,0,0) is also feasible and has zero ones, so this option is not correct.

Option 2: 'all variables can be 0 at the same time.' The assignment (0,0,0) yields a sum of 0, which satisfies W1 + W2 + W3 ≤ 2. Therefore, this statement is true.

Option 3: 'the variables are mutually exclusive.' Mutual exclusivity would mean at most one of W1, W2, W3 can be 1 in any feasible solution. But since two 1’s are allowed (sum ≤ 2), the variables are not mutually exclusive. This makes the statement false.

Option 4: 'none of the above.' Since option 2 is true, this option is false.

In summary, evaluating each option against the given constraint shows the only statement that holds under all feasible assignments is that all zeros is allowed, while the other statements contradict the constraint or its consequences.

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?Single choice

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