If the right-hand side of the constraint X1 + X2 ≤ 4 is increased by 1, how does the feasible region change?

• A. Shrinks
• B. Expands
• C. No change
• D. It depends on the objective

Answer: (B)

Increasing the right-hand side of a ≤ constraint loosens that constraint, so the feasible region grows. Here, points satisfy X1 + X2 ≤ 4. If you raise the limit to 5, the constraint becomes X1 + X2 ≤ 5, which includes all previous feasible points plus new ones between the lines X1 + X2 = 4 and X1 + X2 = 5. The boundary shifts outward, expanding the region (toward larger sums of X1 and X2). The objective affects which feasible point is chosen, not which points are feasible, so the answer isn’t about the objective.