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