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.