Finding Feasible Solutions To A Linear Programming Worksheet - Columbia University In The City Of New York Page 5

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Standard Form
z =
x
M a
(6)
a = 5
x + e
(7)
Note that this is not really in standard form. a is on the left hand side
of a constraint, and the right hand side of the objective function. We
can’t allow this, so we use the equation to get rid of the a in the objective
function. The objective function is now
x
M a =
x
M (5
x + e)
=
5M + (M
1)x
M e
Rewriting, we obtain
z =
5M
+ (M
1)x
M e
(8)
a =
5
x +
e
(9)
Now we have a basic feasible solution (x, e, a) = (0, 0, 5) and can continue
with the simplex algorithm.

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