Chapter 5, Problem 17RE

In Exercises 9-18, 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.

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

Subject to $x+y\ge 30$

$x+z\ge 20$

$x+y\ge 20$

$x+y-w\le 10$

$y+z-w\le 10$

$x\ge 0,y\ge 0,z\ge 0,w\ge 0$.