Put problems 1 and 2 below into the row 0 form described in class and then use the Simplex method to find an optimal solution. You are free to use a calculator or computer to perform any of the necessary calculations, but in order to receive full credit you must show the tableau for each iteration. At each iteration you must also show the current basic feasible solution (i.e. give the value of each variable), resulting objective function value and indicate which variables will enter and leave the basis.

1)

max 200 x1 + 300 x2

subject to

3 x1 + 2 x2 + x3 = 100

2 x1 + 4 x2 + x4 = 120

x1 + x2 + x5 = 45

All variables non-negative

Start with x3, x4 and x5 basic, x1 and x2 non-basic.

2)

max 4 x1 + x2

subject to

8 x1 + 2 x2+x3= 16

5 x1 + 2 x2 + x4 = 12

All variables non-negative

Start with x3 and x4 basic, x1 and x2 non-basic.