[10 pts.] Solve this problem using simplex method:

Max z = x1 + 9x2 + x3

Subject to:

x1 + 2x2 + 3x3 9

3x1 + 2x2 + 2x3 15

x1, x2, x3 0

And then find:

a- Find the shadow prices.

b- Find the scarce and abundant resources.

c- If we change the right hand in the first constrains from 9 to 12, what the

impact on the availability of the solution.

d- Find the maximum and minimum change in Z, if change the return value of x2 .

e- What happen if add a new constraint 3x1 + 2x2 + 3x3 15