Solve the following linear programming problems as directed. Put in a box the values of all the variables you use in your solution, as well as the optimal value of the objective function. SOLVE BY HAND.

a) SIMPLEX METHOD

Max Z = 11X1 + 10X2

s.t.

2 X1 + X2 <= 150

4 X1 + 3 X2 <= 200

X1 + 6 X2 <= 175

X1, X2 >= 0

b) GRAPHIC METHOD (do not forget to indicate the feasible region)

Min Z = 30 X1 + 25 X2

s.t.

7 X1 + 4 X2 >= 28

5 X1 + 8 X2 >= 40

X1 + 4 X2 >= 12

X1, X2 >= 0