Solve the problem
maximise x0 = -x1 -2x2 - x3
subject to
x1 + 3x2 -x3 ⩾ 6
-0.5x1 + x2 ⩾ 1
x1, x2,x3⩾ 0
(a) by introducing artificial variables and using the 'big M' method;
(b) by using the dual simplex method.