Homework #2 Solutions, Due: Thursday, March 8, 2007
x1 | x2 | x3 | -1 | |
-2 | 3 | -1 | -9 | = -x4 |
2 | -2 | 5 | 0 | = -x5 |
4 | 3 | -7 | 5 | --> max |
Choose -1 in Row 1, Column 3 as the Pivot Entry to avoid fractions:
x1 | x2 | x4 | -1 | |
2 | -3 | -1 | 9 | = -x3 |
-8 | 13 | 5 | -45 | = -x5 |
18 | -18 | -7 | 68 | --> max |
Two choices for Pivot Entry: 2 in Row 1 or -8 in Row 2.
Compare each (Bi/Ai):
(-45/-8) = 5.625
9/2 = 4.5
5.625 > 4.5, So choose 2 as the Pivot Entry:
x3 | x2 | x4 | -1 | |
1/2 | -3/2 | -1/2 | 9/2 | = -x1 |
4 | 1 | 1 | -9 | = -x5 |
-9 | 9 | 2 | -13 | --> max |
Row 2 is a Bad Row, therefore the LP is infeasible.