Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. HINT [See Example 1.] (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.)

Maximize p = x + 2y subject to
x + 4y ≤ 18
4x + y ≤ 12
x ≥ 0, y ≥ 0.
p =
(x, y) =