Solve both problems graphically and using the simplex method. Find the dual problem for the primal problem. Solve for the dual prices of the dual problem both graphically and with the simplex method.

Problem #1

max Z=500x1 + 300x2

subject to

15x1+5x2 <=300

10x1 + 6x2 <=240

8x1 + 12x2 <=450

and x1>=0, X2>=0

Problem #2)

min z=40x1 + 50x2

subject to

2x1 + 3x2>=30

x1 + x2>=12

2x1 + x2 >=20

and x1>=0, x2>=0