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Test Cases of Programming Task 1: "Introduction to Optimization"

Test Case 1

Optimization problem:

max z = 4.00x₁ + 5.00x₂

Subject to constraints:

2.00x₁ + 4.00x₂ ≤ 560.00  
1.00x₁ + 1.00x₂ ≤ 170.00  
2.00x₁ + 1.00x₂ ≤ 300.00
Iteration Simplex Tableau Pivot Element Selected Row and Column
1 2.00x₁ + 4.00x₂ + 1.00s₁ + 0.00s₂ + 0.00s₃ = 560.00
1.00x₁ + 1.00x₂ + 0.00s₁ + 1.00s₂ + 0.00s₃ = 170.00
2.00x₁ + 1.00x₂ + 0.00s₁ + 0.00s₂ + 1.00s₃ = 300.00
-4.00x₁ + -5.00x₂ + 0.00s₁ + 0.00s₂ + 0.00s₃ = 0.00		 2,00x1 + 4,00x2 + 1,00s1 + 0,00s2 + 0,00s3 = 560,00
1,00x1 + 1,00x2 + 0,00s1 + 1,00s2 + 0,00s3 = 170,00
2,00x1 + 1,00x2 + 0,00s1 + 0,00s2 + 1,00s3 = 300,00
-4,00x1 + -5,00x2 + 0,00s1 + 0,00s2 + 0,00s3 = 0,00		 Row 1, Column 2
2 0.50x₁ + 1.00x₂ + 0.25s₁ + 0.00s₂ + 0.00s₃ = 140.00
0.50x₁ + 0.00x₂ + -0.25s₁ + 1.00s₂ + 0.00s₃ = 30.00
1.50x₁ + 0.00x₂ + -0.25s₁ + 0.00s₂ + 1.00s₃ = 160.00
-1.50x₁ + 0.00x₂ + 1.25s₁ + 0.00s₂ + 0.00s₃ = 700.00		 0,50x1 + 1,00x2 + 0,25s1 + 0,00s2 + 0,00s3 = 140,00
0,50x1 + 0,00x2 + -0,25s1 + 1,00s2 + 0,00s3 = 30,00
1,50x1 + 0,00x2 + -0,25s1 + 0,00s2 + 1,00s3 = 160,00
-1,50x1 + 0,00x2 + 1,25s1 + 0,00s2 + 0,00s3 = 700,00		 Row 2, Column 1
3 0.00x₁ + 1.00x₂ + 0.50s₁ + -1.00s₂ + 0.00s₃ = 110.00
1.00x₁ + 0.00x₂ + -0.50s₁ + 2.00s₂ + 0.00s₃ = 60.00
0.00x₁ + 0.00x₂ + 0.50s₁ + -3.00s₂ + 1.00s₃ = 70.00
0.00x₁ + 0.00x₂ + 0.50s₁ + 3.00s₂ + 0.00s₃ = 790.00		 — —
Solution x₁ = 60.00, x₂ = 110.00 Objective function value: 790.00

Test Case 2

Optimization problem:

max z = 40.00x₁ + 30.00x₂

Subject to constraints:

1.00x₁ + 1.00x₂ ≤ 12.00  
2.00x₁ + 1.00x₂ ≤ 16.00  
-1.00x₁ + 0.00x₂ ≤ 0.00  
0.00x₁ + -1.00x₂ ≤ 0.00
Iteration Simplex Tableau Pivot Element Selected Row and Column
1 1.00x₁ + 1.00x₂ + 1.00s₁ + 0.00s₂ + 0.00s₃ + 0.00s₄ = 12.00
2.00x₁ + 1.00x₂ + 0.00s₁ + 1.00s₂ + 0.00s₃ + 0.00s₄ = 16.00
-1.00x₁ + 0.00x₂ + 0.00s₁ + 0.00s₂ + 1.00s₃ + 0.00s₄ = 0.00
0.00x₁ + -1.00x₂ + 0.00s₁ + 0.00s₂ + 0.00s₃ + 1.00s₄ = 0.00
-40.00x₁ + -30.00x₂ + 0.00s₁ + 0.00s₂ + 0.00s₃ + 0.00s₄ = 0.00		 1,00x1 + 1,00x2 + 1,00s1 + 0,00s2 + 0,00s3 + 0,00s4 = 12,00
2,00x1 + 1,00x2 + 0,00s1 + 1,00s2 + 0,00s3 + 0,00s4 = 16,00
-1,00x1 + 0,00x2 + 0,00s1 + 0,00s2 + 1,00s3 + 0,00s4 = 0,00
0,00x1 + -1,00x2 + 0,00s1 + 0,00s2 + 0,00s3 + 1,00s4 = 0,00
-40,00x1 + -30,00x2 + 0,00s1 + 0,00s2 + 0,00s3 + 0,00s4 = 0,00		 Row 2, Column 1
2 0.00x₁ + 0.50x₂ + 1.00s₁ + -0.50s₂ + 0.00s₃ + 0.00s₄ = 4.00
1.00x₁ + 0.50x₂ + 0.00s₁ + 0.50s₂ + 0.00s₃ + 0.00s₄ = 8.00
0.00x₁ + 0.50x₂ + 0.00s₁ + 0.50s₂ + 1.00s₃ + 0.00s₄ = 8.00
0.00x₁ + -1.00x₂ + 0.00s₁ + 0.00s₂ + 0.00s₃ + 1.00s₄ = 0.00
0.00x₁ + -10.00x₂ + 0.00s₁ + 20.00s₂ + 0.00s₃ + 0.00s₄ = 320.00		 0,00x1 + 0,50x2 + 1,00s1 + -0,50s2 + 0,00s3 + 0,00s4 = 4,00
1,00x1 + 0,50x2 + 0,00s1 + 0,50s2 + 0,00s3 + 0,00s4 = 8,00
0,00x1 + 0,50x2 + 0,00s1 + 0,50s2 + 1,00s3 + 0,00s4 = 8,00
0,00x1 + -1,00x2 + 0,00s1 + 0,00s2 + 0,00s3 + 1,00s4 = 0,00
0,00x1 + -10,00x2 + 0,00s1 + 20,00s2 + 0,00s3 + 0,00s4 = 320,00		 Row 1, Column 2
3 0.00x₁ + 1.00x₂ + 2.00s₁ + -1.00s₂ + 0.00s₃ + 0.00s₄ = 8.00
1.00x₁ + 0.00x₂ + -1.00s₁ + 1.00s₂ + 0.00s₃ + 0.00s₄ = 4.00
0.00x₁ + 0.00x₂ + -1.00s₁ + 1.00s₂ + 1.00s₃ + 0.00s₄ = 4.00
0.00x₁ + 0.00x₂ + 2.00s₁ + -1.00s₂ + 0.00s₃ + 1.00s₄ = 8.00
0.00x₁ + 0.00x₂ + 20.00s₁ + 10.00s₂ + 0.00s₃ + 0.00s₄ = 400.00		 — —
Solution x₁ = 4.00, x₂ = 8.00 Objective function value: 400.00

Test Case 3

Optimization problem:

max z = 3.00x₁ + 5.00x₂ + 4.00x₃

Subject to constraints:

2.00x₁ + 3.00x₂ + 0.00x₃ ≤ 8.00  
0.00x₁ + 2.00x₂ + 5.00x₃ ≤ 10.00  
3.00x₁ + 2.00x₂ + 4.00x₃ ≤ 15.00  
-1.00x₁ + 0.00x₂ + 0.00x₃ ≤ 0.00
0.00x₁ - 1.00x₂ + 0.00x₃ ≤ 0.00
0.00x₁ + 0.00x₂ - 1.00x₃ ≤ 0.00
Iteration Simplex Tableau Pivot Element Selected Row and Column
1 2,00x1 + 3,00x2 + 0,00x3 + 1,00s1 + 0,00s2 + 0,00s3 + 0,00s4 + 0,00s5 + 0,00s6 = 8,00
0,00x1 + 2,00x2 + 5,00x3 + 0,00s1 + 1,00s2 + 0,00s3 + 0,00s4 + 0,00s5 + 0,00s6 = 10,00
3,00x1 + 2,00x2 + 4,00x3 + 0,00s1 + 0,00s2 + 1,00s3 + 0,00s4 + 0,00s5 + 0,00s6 = 15,00
-1,00x1 + 0,00x2 + 0,00x3 + 0,00s1 + 0,00s2 + 0,00s3 + 1,00s4 + 0,00s5 + 0,00s6 = 0,00 0,00x1 + -1,00x2 + 0,00x3 + 0,00s1 + 0,00s2 + 0,00s3 + 0,00s4 + 1,00s5 + 0,00s6 = 0,00
0,00x1 + 0,00x2 + -1,00x3 + 0,00s1 + 0,00s2 + 0,00s3 + 0,00s4 + 0,00s5 + 1,00s6 = 0,00
-3,00x1 + -5,00x2 + -4,00x3 + 0,00s1 + 0,00s2 + 0,00s3 + 0,00s4 + 0,00s5 + 0,00s6 = 0,00		 2,00x1 + 3,00x2 + 0,00x3 + 1,00s1 + 0,00s2 + 0,00s3 + 0,00s4 + 0,00s5 + 0,00s6 = 8,00
0,00x1 + 2,00x2 + 5,00x3 + 0,00s1 + 1,00s2 + 0,00s3 + 0,00s4 + 0,00s5 + 0,00s6 = 10,00
3,00x1 + 2,00x2 + 4,00x3 + 0,00s1 + 0,00s2 + 1,00s3 + 0,00s4 + 0,00s5 + 0,00s6 = 15,00
-1,00x1 + 0,00x2 + 0,00x3 + 0,00s1 + 0,00s2 + 0,00s3 + 1,00s4 + 0,00s5 + 0,00s6 = 0,00
0,00x1 + -1,00x2 + 0,00x3 + 0,00s1 + 0,00s2 + 0,00s3 + 0,00s4 + 1,00s5 + 0,00s6 = 0,00
0,00x1 + 0,00x2 + -1,00x3 + 0,00s1 + 0,00s2 + 0,00s3 + 0,00s4 + 0,00s5 + 1,00s6 = 0,00
-3,00x1 + -5,00x2 + -4,00x3 + 0,00s1 + 0,00s2 + 0,00s3 + 0,00s4 + 0,00s5 + 0,00*s6 = 0,00		 Row 1, Column 2
2 0,67x1 + 1,00x2 + 0,00x3 + 0,33s1 + 0,00s2 + 0,00s3 + 0,00s4 + 0,00s5 + 0,00s6 = 2,67
-1,33x1 + 0,00x2 + 5,00x3 + -0,67s1 + 1,00s2 + 0,00s3 + 0,00s4 + 0,00s5 + 0,00s6 = 4,67
1,67x1 + 0,00x2 + 4,00x3 + -0,67s1 + 0,00s2 + 1,00s3 + 0,00s4 + 0,00s5 + 0,00s6 = 9,67
-1,00x1 + 0,00x2 + 0,00x3 + 0,00s1 + 0,00s2 + 0,00s3 + 1,00s4 + 0,00s5 + 0,00s6 = 0,00
0,67x1 + 0,00x2 + 0,00x3 + 0,33s1 + 0,00s2 + 0,00s3 + 0,00s4 + 1,00s5 + 0,00s6 = 2,67
0,00x1 + 0,00x2 + -1,00x3 + 0,00s1 + 0,00s2 + 0,00s3 + 0,00s4 + 0,00s5 + 1,00s6 = 0,00
0,33x1 + 0,00x2 + -4,00x3 + 1,67s1 + 0,00s2 + 0,00s3 + 0,00s4 + 0,00s5 + 0,00s6 = 13,33		 0,67x1 + 1,00x2 + 0,00x3 + 0,33s1 + 0,00s2 + 0,00s3 + 0,00s4 + 0,00s5 + 0,00s6 = 2,67
-1,33x1 + 0,00x2 + 5,00x3 + -0,67s1 + 1,00s2 + 0,00s3 + 0,00s4 + 0,00s5 + 0,00s6 = 4,67
1,67x1 + 0,00x2 + 4,00x3 + -0,67s1 + 0,00s2 + 1,00s3 + 0,00s4 + 0,00s5 + 0,00s6 = 9,67
-1,00x1 + 0,00x2 + 0,00x3 + 0,00s1 + 0,00s2 + 0,00s3 + 1,00s4 + 0,00s5 + 0,00s6 = 0,00
0,67x1 + 0,00x2 + 0,00x3 + 0,33s1 + 0,00s2 + 0,00s3 + 0,00s4 + 1,00s5 + 0,00s6 = 2,67
0,00x1 + 0,00x2 + -1,00x3 + 0,00s1 + 0,00s2 + 0,00s3 + 0,00s4 + 0,00s5 + 1,00s6 = 0,00
0,33x1 + 0,00x2 + -4,00x3 + 1,67s1 + 0,00s2 + 0,00s3 + 0,00s4 + 0,00s5 + 0,00*s6 = 13,33		 Row 1, Column 2
3 0,67x1 + 1,00x2 + 0,00x3 + 0,33s1 + 0,00s2 + 0,00s3 + 0,00s4 + 0,00s5 + 0,00s6 = 2,67
-0,27x1 + 0,00x2 + 1,00x3 + -0,13s1 + 0,20s2 + 0,00s3 + 0,00s4 + 0,00s5 + 0,00s6 = 0,93
2,73x1 + 0,00x2 + 0,00x3 + -0,13s1 + -0,80s2 + 1,00s3 + 0,00s4 + 0,00s5 + 0,00s6 = 5,93
-1,00x1 + 0,00x2 + 0,00x3 + 0,00s1 + 0,00s2 + 0,00s3 + 1,00s4 + 0,00s5 + 0,00s6 = 0,00 0,67x1 + 0,00x2 + 0,00x3 + 0,33s1 + 0,00s2 + 0,00s3 + 0,00s4 + 1,00s5 + 0,00s6 = 2,67
-0,27x1 + 0,00x2 + 0,00x3 + -0,13s1 + 0,20s2 + 0,00s3 + 0,00s4 + 0,00s5 + 1,00s6 = 0,93
-0,73x1 + 0,00x2 + 0,00x3 + 1,13s1 + 0,80s2 + 0,00s3 + 0,00s4 + 0,00s5 + 0,00s6 = 17,07		 0,67x1 + 1,00x2 + 0,00x3 + 0,33s1 + 0,00s2 + 0,00s3 + 0,00s4 + 0,00s5 + 0,00s6 = 2,67
-0,27x1 + 0,00x2 + 1,00x3 + -0,13s1 + 0,20s2 + 0,00s3 + 0,00s4 + 0,00s5 + 0,00s6 = 0,93
2,73x1 + 0,00x2 + 0,00x3 + -0,13s1 + -0,80s2 + 1,00s3 + 0,00s4 + 0,00s5 + 0,00s6 = 5,93
-1,00x1 + 0,00x2 + 0,00x3 + 0,00s1 + 0,00s2 + 0,00s3 + 1,00s4 + 0,00s5 + 0,00s6 = 0,00
0,67x1 + 0,00x2 + 0,00x3 + 0,33s1 + 0,00s2 + 0,00s3 + 0,00s4 + 1,00s5 + 0,00s6 = 2,67
-0,27x1 + 0,00x2 + 0,00x3 + -0,13s1 + 0,20s2 + 0,00s3 + 0,00s4 + 0,00s5 + 1,00s6 = 0,93
-0,73x1 + 0,00x2 + 0,00x3 + 1,13s1 + 0,80s2 + 0,00s3 + 0,00s4 + 0,00s5 + 0,00*s6 = 17,07		 Row 3, Column 1
4 0,00x1 + 1,00x2 + 0,00x3 + 0,37s1 + 0,20s2 + -0,24s3 + 0,00s4 + 0,00s5 + 0,00s6 = 1,22
0,00x1 + 0,00x2 + 1,00x3 + -0,15s1 + 0,12s2 + 0,10s3 + 0,00s4 + 0,00s5 + 0,00s6 = 1,51
1,00x1 + 0,00x2 + 0,00x3 + -0,05s1 + -0,29s2 + 0,37s3 + 0,00s4 + 0,00s5 + 0,00s6 = 2,17
0,00x1 + 0,00x2 + 0,00x3 + -0,05s1 + -0,29s2 + 0,37s3 + 1,00s4 + 0,00s5 + 0,00s6 = 2,17
0,00x1 + 0,00x2 + 0,00x3 + 0,37s1 + 0,20s2 + -0,24s3 + 0,00s4 + 1,00s5 + 0,00s6 = 1,22
0,00x1 + 0,00x2 + 0,00x3 + -0,15s1 + 0,12s2 + 0,10s3 + 0,00s4 + 0,00s5 + 1,00s6 = 1,51
0,00x1 + 0,00x2 + 0,00x3 + 1,10s1 + 0,59s2 + 0,27s3 + 0,00s4 + 0,00s5 + 0,00*s6 = 18,66		 — —
Solution x₁ = 2,17073, x₂ = 1,21951, x₃ = 1,51220 Objective function value: 18,65854

Test Case 4

Optimization problem:

max z = 3.00x₁ + 2.00x₂

Subject to constraints:

2.00x₁ + 1.00x₂ ≤ 18.00  
2.00x₁ + 3.00x₂ ≤ 42.00  
3.00x₁ + 1.00x₂ ≤ 24.00  
-1.00x₁ + 0.00x₂ ≤ 0.00
0.00x₁ - 1.00x₂ ≤ 0.00
Iteration Simplex Tableau Pivot Element Selected Row and Column
1 2,00x1 + 1,00x2 + 1,00s1 + 0,00s2 + 0,00s3 + 0,00s4 + 0,00s5 = 18,00
2,00x1 + 3,00x2 + 0,00s1 + 1,00s2 + 0,00s3 + 0,00s4 + 0,00s5 = 42,00
3,00x1 + 1,00x2 + 0,00s1 + 0,00s2 + 1,00s3 + 0,00s4 + 0,00s5 = 24,00
-1,00x1 + 0,00x2 + 0,00s1 + 0,00s2 + 0,00s3 + 1,00s4 + 0,00s5 = 0,00
0,00x1 + -1,00x2 + 0,00s1 + 0,00s2 + 0,00s3 + 0,00s4 + 1,00s5 = 0,00
-3,00x1 + -2,00x2 + 0,00s1 + 0,00s2 + 0,00s3 + 0,00s4 + 0,00s5 = 0,00		 2,00x1 + 1,00x2 + 1,00s1 + 0,00s2 + 0,00s3 + 0,00s4 + 0,00s5 = 18,00
2,00x1 + 3,00x2 + 0,00s1 + 1,00s2 + 0,00s3 + 0,00s4 + 0,00s5 = 42,00
3,00x1 + 1,00x2 + 0,00s1 + 0,00s2 + 1,00s3 + 0,00s4 + 0,00s5 = 24,00
-1,00x1 + 0,00x2 + 0,00s1 + 0,00s2 + 0,00s3 + 1,00s4 + 0,00s5 = 0,00
0,00x1 + -1,00x2 + 0,00s1 + 0,00s2 + 0,00s3 + 0,00s4 + 1,00s5 = 0,00
-3,00x1 + -2,00x2 + 0,00s1 + 0,00s2 + 0,00s3 + 0,00s4 + 0,00s5 = 0,00		 Row 3, Column 1
2 0,00x1 + 0,33x2 + 1,00s1 + 0,00s2 + -0,67s3 + 0,00s4 + 0,00s5 = 2,00
0,00x1 + 2,33x2 + 0,00s1 + 1,00s2 + -0,67s3 + 0,00s4 + 0,00s5 = 26,00
1,00x1 + 0,33x2 + 0,00s1 + 0,00s2 + 0,33s3 + 0,00s4 + 0,00s5 = 8,00
0,00x1 + 0,33x2 + 0,00s1 + 0,00s2 + 0,33s3 + 1,00s4 + 0,00s5 = 8,00
0,00x1 + -1,00x2 + 0,00s1 + 0,00s2 + 0,00s3 + 0,00s4 + 1,00s5 = 0,00
0,00x1 + -1,00x2 + 0,00s1 + 0,00s2 + 1,00s3 + 0,00s4 + 0,00s5 = 24,00		 0,00x1 + 0,33x2 + 1,00s1 + 0,00s2 + -0,67s3 + 0,00s4 + 0,00s5 = 2,00
0,00x1 + 2,33x2 + 0,00s1 + 1,00s2 + -0,67s3 + 0,00s4 + 0,00s5 = 26,00
1,00x1 + 0,33x2 + 0,00s1 + 0,00s2 + 0,33s3 + 0,00s4 + 0,00s5 = 8,00
0,00x1 + 0,33x2 + 0,00s1 + 0,00s2 + 0,33s3 + 1,00s4 + 0,00s5 = 8,00
0,00x1 + -1,00x2 + 0,00s1 + 0,00s2 + 0,00s3 + 0,00s4 + 1,00s5 = 0,00
0,00x1 + -1,00x2 + 0,00s1 + 0,00s2 + 1,00s3 + 0,00s4 + 0,00s5 = 24,00		 Row 1, Column 2
3 0,00x1 + 1,00x2 + 3,00s1 + 0,00s2 + -2,00s3 + 0,00s4 + 0,00s5 = 6,00
0,00x1 + 0,00x2 + -7,00s1 + 1,00s2 + 4,00s3 + 0,00s4 + 0,00s5 = 12,00
1,00x1 + 0,00x2 + -1,00s1 + 0,00s2 + 1,00s3 + 0,00s4 + 0,00s5 = 6,00
0,00x1 + 0,00x2 + -1,00s1 + 0,00s2 + 1,00s3 + 1,00s4 + 0,00s5 = 6,00
0,00x1 + 0,00x2 + 3,00s1 + 0,00s2 + -2,00s3 + 0,00s4 + 1,00s5 = 6,00
0,00x1 + 0,00x2 + 3,00s1 + 0,00s2 + -1,00s3 + 0,00s4 + 0,00s5 = 30,00		 0,00x1 + 1,00x2 + 3,00s1 + 0,00s2 + -2,00s3 + 0,00s4 + 0,00s5 = 6,00
0,00x1 + 0,00x2 + -7,00s1 + 1,00s2 + 4,00s3 + 0,00s4 + 0,00s5 = 12,00
1,00x1 + 0,00x2 + -1,00s1 + 0,00s2 + 1,00s3 + 0,00s4 + 0,00s5 = 6,00
0,00x1 + 0,00x2 + -1,00s1 + 0,00s2 + 1,00s3 + 1,00s4 + 0,00s5 = 6,00
0,00x1 + 0,00x2 + 3,00s1 + 0,00s2 + -2,00s3 + 0,00s4 + 1,00s5 = 6,00
0,00x1 + 0,00x2 + 3,00s1 + 0,00s2 + -1,00s3 + 0,00s4 + 0,00s5 = 30,00		 Row 2, Column 5
4 0,00x1 + 1,00x2 + -0,50s1 + 0,50s2 + 0,00s3 + 0,00s4 + 0,00s5 = 12,00
0,00x1 + 0,00x2 + -1,75s1 + 0,25s2 + 1,00s3 + 0,00s4 + 0,00s5 = 3,00
1,00x1 + 0,00x2 + 0,75s1 + -0,25s2 + 0,00s3 + 0,00s4 + 0,00s5 = 3,00
0,00x1 + 0,00x2 + 0,75s1 + -0,25s2 + 0,00s3 + 1,00s4 + 0,00s5 = 3,00
0,00x1 + 0,00x2 + -0,50s1 + 0,50s2 + 0,00s3 + 0,00s4 + 1,00s5 = 12,00
0,00x1 + 0,00x2 + 1,25s1 + 0,25s2 + 0,00s3 + 0,00s4 + 0,00s5 = 33,00		 — —
Solution x₁ = 3,00000, x₂ = 12,00000 Objective function value: 33,00000

Test Case 5

Optimization problem:

max z = 4.00x₁ + 1.00x₂

Subject to constraints:

1.00x₁ + 1.00x₂ ≤ 50.00  
3.00x₁ + 1.00x₂ ≤ 90.00  
-1.00x₁ + 0.00x₂ ≤ 0.00  
0.00x₁ + -1.00x₂ ≤ 0.00
Iteration Simplex Tableau Pivot Element Selected Row and Column
1 1,00x1 + 1,00x2 + 1,00s1 + 0,00s2 + 0,00s3 + 0,00s4 = 50,00
3,00x1 + 1,00x2 + 0,00s1 + 1,00s2 + 0,00s3 + 0,00s4 = 90,00
-1,00x1 + 0,00x2 + 0,00s1 + 0,00s2 + 1,00s3 + 0,00s4 = 0,00
0,00x1 + -1,00x2 + 0,00s1 + 0,00s2 + 0,00s3 + 1,00s4 = 0,00
-4,00x1 + -1,00x2 + 0,00s1 + 0,00s2 + 0,00s3 + 0,00s4 = 0,00		 1,00x1 + 1,00x2 + 1,00s1 + 0,00s2 + 0,00s3 + 0,00s4 = 50,00
3,00x1 + 1,00x2 + 0,00s1 + 1,00s2 + 0,00s3 + 0,00s4 = 90,00
-1,00x1 + 0,00x2 + 0,00s1 + 0,00s2 + 1,00s3 + 0,00s4 = 0,00
0,00x1 + -1,00x2 + 0,00s1 + 0,00s2 + 0,00s3 + 1,00s4 = 0,00
-4,00x1 + -1,00x2 + 0,00s1 + 0,00s2 + 0,00s3 + 0,00s4 = 0,00		 Row 2, Column 1
2 0,00x1 + 0,67x2 + 1,00s1 + -0,33s2 + 0,00s3 + 0,00s4 = 20,00
1,00x1 + 0,33x2 + 0,00s1 + 0,33s2 + 0,00s3 + 0,00s4 = 30,00
0,00x1 + 0,33x2 + 0,00s1 + 0,33s2 + 1,00s3 + 0,00s4 = 30,00
0,00x1 + -1,00x2 + 0,00s1 + 0,00s2 + 0,00s3 + 1,00s4 = 0,00
0,00x1 + 0,33x2 + 0,00s1 + 1,33s2 + 0,00s3 + 0,00s4 = 120,00		 — —
Solution x₁ = 30,00000, x₂ = 0,00000 Objective function value: 120,00000

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