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Home > Operation Research > Simplex method calculator
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Solve the Linear programming problem using
Simplex method calculator

New: You can find Entering variable using `Z` or `Z_j-C_j` or `C_j-Z_j` Row (developed on 16.03.2026)
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Total Variables : Total Constraints :
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Entering variable using `Z` or `Z_j-C_j` or `C_j-Z_j` Row :
  1. max Z = 3x1 + 5x2 + 4x3
    subject to
    2x1 + 3x2 <= 8
    2x2 + 5x3 <= 10
    3x1 + 2x2 + 4x3 <= 15
    and x1,x2,x3 >= 0;
  2. max Z = 5x1 + 10x2 + 8x3
    subject to
    3x1 + 5x2 + 2x3 <= 60
    4x1 + 4x2 + 4x3 <= 72
    2x1 + 4x2 + 5x3 <= 100
    and x1,x2,x3 >= 0;
  3. max Z = 4x1 + 3x2
    subject to
    2x1 + x2 <= 1000
    x1 + x2 <= 800
    x1 <= 400
    x2 <= 700
    and x1,x2 >= 0;
  4. min Z = x1 + x2
    subject to
    2x1 + 4x2 >= 4
    x1 + 7x2 >= 7
    and x1,x2 >= 0;
  5. min Z = 600x1 + 500x2
    subject to
    2x1 + x2 >= 80
    x1 + 2x2 >= 60
    and x1,x2 >= 0;
  6. min Z = 5x1 + 3x2
    subject to
    2x1 + 4x2 <= 12
    2x1 + 2x2 = 10
    5x1 + 2x2 >= 10
    and x1,x2 >= 0;
  7. 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;
  8. max Z = 3x1 + 9x2
    subject to
    x1 + 4x2 <= 8
    x1 + 2x2 <= 4
    and x1,x2 >= 0;
  9. max Z = 3x1 + 2x2 + x3
    subject to
    2x1 + 5x2 + x3 = 12
    3x1 + 4x2 = 11
    and x2,x3 >= 0; x1 unrestricted in sign
  10. max Z = 3x1 + 3x2 + 2x3 + x4
    subject to
    2x1 + 2x2 + 5x3 + x4 = 12
    3x1 + 3x2 + 4x3 = 11
    and x1,x2,x3,x4 >= 0;
  11. max Z = 6x1 + 4x2
    subject to
    2x1 + 3x2 <= 30
    3x1 + 2x2 <= 24
    x1 + x2 >= 3
    and x1,x2 >= 0;
  12. max Z = 3x1 + 5x2
    subject to
    x1 - 2x2 <= 6
    x1 <= 10
    x2 >= 1
    and x1,x2 >= 0;
  13. max Z = 6x1 + 4x2
    subject to
    x1 + x2 <= 5
    x2 >= 8
    and x1,x2 >= 0;
  14. max Z = 6x1 + 4x2
    subject to
    -x1 - x2 >= -5
    x2 >= 8
    and x1,x2 >= 0;
Min ratios are same then exit row option :
Display solution steps in :
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Entering variable using `Z` improved on 27.04.2026.

For wrong solution or any other output display format or any other new solution method of simplex, please submit the feedback form. So I will try my best to develop it soon.
 


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