I may not be understanding the Simplex algorithm very well, or even if my problem is a problem at all so I'll use an example.
Given an optimization problem:
LP PB:
min z = +2x1 +3x2
st. +3x1 +2x2 = 14
+2x1 -4x2 >= 2
+4x1 +3x2 <= 19
x1, x2 >= 0
Convert to std form:
STD LP PB:
min z = +2x1 +3x2
st. +3x1 +2x2 = 14
+2x1 -4x2 -x3 = 2
+4x1 +3x2 +x4 = 19
x1, x2, x3, x4 >= 0
After applying Simplex and the 2-Phase method for generating the initial basis I get the following solution:
x1 = 4.666...
x2 = 0
x3 = 7.333...
x4 = 0.333...
With the basis being {x1, x3, x4}
obviously.
In this case, since the original problem simply "asks" to find the optimal values for x1
and x2
, do I just take the values of x1
and x2
from the solution given by simplex and that's it? Or how do you get the values for the original problem?