Final Answer:
The correct answer is C. (2, 2), where the maximum value of the objective function f = 5x + 2y occurs.
Step-by-step explanation:
To find the maximum value of the objective function subject to the given constraints, we can use the method of linear programming. The constraints are x + 2y ≤ 6, x ≥ 0, and y ≥ 0. To determine the optimal solution, we evaluate the objective function f = 5x + 2y at the corner points of the feasible region formed by the intersection of these constraints.
The corner points are obtained by solving the system of equations formed by the constraints. For this problem, the corner points are (0, 3), (2, 2), (3, 1), and (6, 0). Evaluating the objective function at these points, we find that the maximum value occurs at (2, 2), where f = 5(2) + 2(2) = 14.
In conclusion, the correct answer is C. (2, 2), and the maximum value of the objective function is 14. This explanation outlines the steps involved in solving the linear programming problem and identifies the optimal solution.