In the same LP, what is the optimal value of X2?

• A. 6
• B. 7
• C. 0
• D. 5

Answer: (B)

In a linear program with two variables, the optimal solution occurs at a corner (vertex) of the feasible region, where two constraints bind. At that corner, the value of X2 is fixed. If the objective is being maximized, you pick the corner that gives the largest objective value; if it's minimized, you pick the smallest. Here, the best corner for X2 happens when X2 equals seven, because that point lies on the intersection of two binding constraints and yields the highest objective value achievable without violating any constraint. Other feasible corners either have a smaller X2 value or produce a worse objective, so seven is the optimal X2. To verify, solve the pairs of binding constraints to get all corner points, then evaluate the objective at each point and choose the highest (or lowest, if minimizing).