Method
1. Simplex method (BigM method)
2. TwoPhase method
3. Dual simplex method
4. Integer simplex method
5. Graphical method
6. Primal to Dual
7. Branch and Bound method
8. 0-1 Integer programming problem
9. Revised Simplex method
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