Consider the primal problem: maximize z = 5x1 + 12x2 + 4x3 subject to x1 + 2x2 + x3 = 10, 2x1 − x2 + 3x3 = 8, x1, x2, x3 ≥ 0. Its dual is: minimize w = 10y1 + 8y2 subject to y1 + 2y2 ≥ 5, 2y1 − y2 ≥ 12, y1 + 3y2 ≥ 4. Which of the following is correct?

1. Ay1 ≥ 0, y2 unrestricted
2. By1 ≥ 0, y2 ≥ 0
3. Cy1 unrestricted, y2 ≥ 0
4. Dy1 unrestricted, y2 restricted

Pick an option to check yourself, or open the answer below.

Show answer & explanation

Correct answer: A. y1 ≥ 0, y2 unrestricted

Explanation

Each primal equality constraint gives an unrestricted dual variable, and each non-negative primal variable gives a ≥ dual constraint (for a maximization primal).

Note: no option is fully correct; the official key (A) is shown. Both primal constraints are equalities, so both dual variables are unrestricted in sign; no option says this. The official key is A.