Linear programming : Simplex Method
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1. Use simplex method to find the answer
Maximize z =3x1+4x2
Subject to x1+x2<=50
X1+x2 >=25
2x1+x2<=60
x1>=0 and x2>=0
2. Use simplex method to find the answer
Minimize w =4y1 + 2y2
Subject to 3y1+y2>=22
y1+4y2 >=26
y1>=0 and y2>=0
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Solution Summary
An LP problem is solved using the Simplex Method. The solution is detailed and well presented.
Solution Preview
1. Use simplex method to find the answer
Maximize z =3x1+4x2
Subject to x1+x2<=50
X1+x2 >=25
2x1+x2<=60
x1>=0 and x2>=0
We first write in the standard form
Maximize z =3x1+4x2+0s1+0s2+0s3
Subject to
x1+x2+s1=50
X1+x2 -s2=25
2x1+x2+s3=60
x1,x2>=0
First table
x1 x2 s1 s2 s3 z Quotients
1 1 1 0 0 0 50 50
1 1 0 -1 0 0 25 25
2 1 0 0 1 0 60 60
-3 -4 0 0 0 1 0
The minimal element in last row =-4 and minimal last column is 25. The grey box is pivotal element
We convert the remaining elements in the pivotal column to zero by following row operations
1. R2 R2
2. R1 R1-R2
3. R3 R3-R2
4. R4 R4 + 4 ...
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