Set 12: Linear Inequalities (Intermediate)

Choice A is correct. Choice A is the correct answer. Evaluate the objective function at the vertices of the feasible region. 1. Vertices: $(0,0)$, $(5,0)$, $(0,5)$. 2. Evaluate at (0,0): $P = 3(0) + 2(0) = 0$ 3. Evaluate at (5,0): $P = 3(5) + 2(0) = 15$ 4. Evaluate at (0,5): $P = 3(0) + 2(5) = 10$ 5. Maximum: The largest value is 15. Strategic Tip: The maximum/minimum in linear programming always occurs at a vertex (corner point). Choice B is incorrect because 10 is not the maximum. Choice C is incorrect because no vertex yields 12. Choice D is incorrect because no vertex yields 13.