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Algorithm and examples
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Method
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Solve the Linear programming problem using
Simplex method calculator
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Type your linear programming problem
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OR
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Total Variables :
Total Constraints :
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Revised Simplex Solution Method :
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Calculate :
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- max Z = 3x1 + 5x2 + 4x3
subject to
2x1 + 3x2 <= 8
2x2 + 5x3 <= 10
3x1 + 2x2 + 4x3 <= 15
and x1,x2,x3 >= 0
- max Z = 5x1 + 10x2 + 8x3
subject to
3x1 + 5x2 + 2x3 <= 60
4x1 + 4x2 + 4x3 <= 72
2x1 + 4x2 + 5x3 <= 100
and x1,x2,x3 >= 0
- max Z = 4x1 + 3x2
subject to
2x1 + x2 <= 1000
x1 + x2 <= 800
x1 <= 400
x2 <= 700
and x1,x2 >= 0
- min Z = x1 + x2
subject to
2x1 + 4x2 >= 4
x1 + 7x2 >= 7
and x1,x2 >= 0
- min Z = 600x1 + 500x2
subject to
2x1 + x2 >= 80
x1 + 2x2 >= 60
and x1,x2 >= 0
- min Z = 5x1 + 3x2
subject to
2x1 + 4x2 <= 12
2x1 + 2x2 = 10
5x1 + 2x2 >= 10
and x1,x2 >= 0
- max Z = x1 + 2x2 + 3x3 - x4
subject to
x1 + 2x2 + 3x3 = 15
2x1 + x2 + 5x3 = 20
x1 + 2x2 + x3 + x4 = 10
and x1,x2,x3,x4 >= 0
- max Z = 3x1 + 9x2
subject to
x1 + 4x2 <= 8
x1 + 2x2 <= 4
and x1,x2 >= 0
- max Z = 3x1 + 2x2 + x3
subject to
2x1 + 5x2 + x3 = 12
3x1 + 4x2 = 11
and x2,x3 >= 0 and x1 unrestricted in sign
- max Z = 3x1 + 3x2 + 2x3 + x4
subject to
2x1 + 2x2 + 5x3 + x4 = 12
3x1 + 3x2 + 4x3 = 11
and x1,x2,x3,x4 >= 0
- max Z = 6x1 + 4x2
subject to
2x1 + 3x2 <= 30
3x1 + 2x2 <= 24
x1 + x2 >= 3
and x1,x2 >= 0
- max Z = 3x1 + 5x2
subject to
x1 - 2x2 <= 6
x1 <= 10
x2 >= 1
and x1,x2 >= 0
- max Z = 6x1 + 4x2
subject to
x1 + x2 <= 5
x2 >= 8
and x1,x2 >= 0
- max Z = 6x1 + 4x2
subject to
-x1 - x2 >= -5
x2 >= 8
and x1,x2 >= 0
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Solution
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Solution provided by AtoZmath.com
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Simplex method calculator
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1. Find solution using simplex method.
Maximize Z = 3x1 + 5x2 + 4x3
subject to the constraints
2x1 + 3x2 ≤ 8
2x2 + 5x3 ≤ 10
3x1 + 2x2 + 4x3 ≤ 15
and x1, x2, x3 ≥ 0
2. Find solution using simplex method.
Maximize Z = 4x1 + 3x2
subject to the constraints
2x1 + x2 ≤ 1000
x1 + x2 ≤ 800
x1 ≤ 400
x2 ≤ 700
and x1,x2 ≥ 0
3. Find solution using BigM (penalty) method.
Minimize Z = 5x1 + 3x2
subject to the constraints
2x1 + 4x2 ≤ 12
2x1 + 2x2 = 10
5x1 + 2x2 ≥ 10
and x1, x2 ≥ 0
4. Find solution using BigM (penalty) method.
Maximize Z = x1 + 2x2 + 3x3 - x4
subject to the constraints
x1 + 2x2 + 3x3 = 15
2x1 + x2 + 5x3 = 20
x1 + 2x2 + x3 + x4 = 10
and x1, x2, x3, x4 ≥ 0
5. Find solution using simplex method (Degeneracy example - Tie for leaving basic variable).
MAX Z = 3x1 + 9x2
subject to
x1 + 4x2 ≤ 8
x1 + 2x2 ≤ 4
and x1,x2 ≥ 0
6. Find solution using simplex method (Unrestricted variable example).
MAX Z = 3x1 + 2x2 + x3
subject to
2x1 + 5x2 + x3 = 12
3x1 + 4x2 = 11
and x2,x3 ≥ 0 and x1 unrestricted in sign
7. Find solution using simplex method (Multiple optimal solution example).
MAX Z = 6x1 + 4x2
subject to
2x1 + 3x2 ≤ 30
3x1 + 2x2 ≤ 24
x1 + x2 ≥ 3
and x1,x2 ≥ 0
8. Find solution using simplex method (Unbounded solution example).
MAX Z = 3x1 + 5x2
subject to
x1 - 2x2 ≤ 6
x1 ≤ 10
x2 ≥ 1
and x1,x2 ≥ 0
9. Find solution using simplex method (Infeasible solution example).
MAX Z = 6x1 + 4x2
subject to
x1 + x2 ≤ 5
x2 ≥ 8
and x1,x2 ≥ 0
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