Submitted by: Submitted by soyti123
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Date Submitted: 10/09/2010 07:05 PM
PROBLEM 5
Let X1 = number of lbs of phosphate to be used in the mixture
X2 = number of lbs of potassium to be used in the mixture
Objective function:
Minimize Cost (C) = P50X1 + P60X2
Subject to:
X1 + X2 = 100
X1 < 30
X2 > 15
X1 > 0
X2 > 0
The complete set of constraints can now be expressed as follows:
X1 + X2 + A1 = 100
X1 + S1 = 30
X2 – S2 + A2 = 15
X1 > 0
X2 > 0
S1 > 0
A1 > 0
A2 > 0
C = 50X1 + 60X2 + OS1 = 100A1 + 100A2
|Cj | | |50 |60 |0 |0 |100 |100 |
|z |2 |3 |0 |0 |0 |0 |0 | |
|s1 |3 |2 |1 |0 |0 |0 |24 | |
|s2 |1 |2 |0 |1 |0 |0 |12 | |
|s3 |0 |1 |0 |0 |1 |0 |4 | |
|s4 |1 |0 |0 |0 |0 |1 |8 | |
At each iteration of the Simplex algorithm, we want to enter a new variable to the basis and remove an old variable from the basis so that the value of z improves (decreases) and the feasibility of all feasible variables is maintained.
The entering variable is determined by examining the reduced costs of the non-basic variables. The reduced cost of a variable represents the...