Solve the given linear programming problem using the simplex method. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. $($Enter EMPTY if the feasible region is empty and UNBOUNDED if the objective function is unbounded.$)$

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

$x+y,80$

$x,+z,70$

$x+y,-w50$

$y+z-w50$

$x0,y0,z0,w0.$

$c=$

$(x,y,z,w)=()$