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.$)$

Minimize c $=$ x $+$ y subject to

x $+3$y $>=4$

$3$x $+$ y $>=4$

x $>=0,$ y $>=0.$