What does the following MiniZinc model print? var 0..3: x;var 1..4: y;constraint y = x + 1;constraint 2*y + 3*x = 12;

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BlackTom AI · Accepted Answer

The question asks what the given MiniZinc model prints. Restating the constraints helps: x is in 0..3, y is in 1..4, y = x + 1, and 2*y + 3*x = 12.
Option a. x = 0; y = 0: This violates the constraint y ∈ 1..4, since y would be 0, and also y must equal x+1, which would require y = 1 when x = 0. So this option is inconsistent with the model.
Option b. x = 2; y = 3: Here x ∈ 0..3 and y ∈ 1..4 are satisfied. Check the relation y = x + 1: 3 = 2 + 1 holds. Check the equation 2*y + 3*x = 12: 2*3 + 3*2 = 6 + 6 = 12, which matches. All constraints are satisfied, so this is a valid solution.
Option c. x = 3; y = 4: While y = x + 1 holds (4 = 3 + 1) and the bounds are satisfied, the equation 2*y + 3*x = 12 would yield 2*4 + 3*3 = 8 + 9 = 17, which does not equal 12. Therefore this option does not satisfy the second equation.
Option d. x = 1; y = 2: This pair satisfies y = x + 1 (2 = 1 + 1) and the bounds, but the equation gives 2*y + 3*x = 2*2 + 3*1 = 4 + 3 = 7, which is not 12. So this option is invalid.
Option e. =====UNSATISFIABLE=====: Since there is at least one assignment (x = 2, y = 3) that satisfies all constraints, the problem is not unsatisfiable. Therefore this option is incorrect.

In summary, option b is the only choice that satisfies all the given constraints, while the others fail either the y = x + 1 relation, the variable bounds, or the linear equation.

What does the following MiniZinc model print? var 0..3: x;var 1..4: y;constraint y = x + 1;constraint 2y + 3x = 12;Single choice

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