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