Finding Feasible Solutions To A Linear Programming Worksheet - Columbia University In The City Of New York Page 3

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Continued
maximize
x
s.t x
e = 5
x, e
0
We deal with this situation, by using an
artifical
variable.
The artificial variable will allow us to easily find a bfs.
Problem:
The artificial variable may allow us to find “solutions” that
are not really solutions to the original LP.
To compensate, we will add the artificial variable to the objective func-
tion with a
very large negative coefficient (big M).
Thus, if we make the artificial variable positive, the objective function will
be extremely negative. But we are maximizing, so we have every incentive
to avoid making the objective function value negative, i.e. we want to avoid
making a positive.
When we are done solving the LP, if the artificial variable is zero, we have
solved the original LP. If it is positive, then we conclude that the original
LP was infeasible.

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