def test_min_feasible2(self):
''' Find optimal solution to min(2x1 + 10x2 + 8x3) such that:
Ax >= b,
x1, x2, x3 >= 0,
A = | 1 1 1|, b = |6|, c = | 2|
| 0 1 2| |8| |10|
|-1 2 2| |4| | 8|
Source: http://college.cengage.com/mathematics/larson/elementary_linear/4e/shared/downloads/c09s4.pdf, Example 2
'''
self.assertDictEqual(
{
'x_1': Fraction(2),
'x_2': Fraction(0),
'x_3': Fraction(4),
's_1': Fraction(0),
's_2': Fraction(5),
's_3': Fraction(0),
'y_1': Fraction(2),
'y_2': Fraction(3),
'y_3': Fraction(0),
'z': Fraction(36)
},
SimplexSolver().run_simplex([[1, 1, 1], [0, 1, 2], [-1, 2, 2]],
[6, 8, 4], [2, 10, 8],
prob='min'))
def test_max_feasible5(self):
''' Find optimal solution to max(11x1 + 16x2 + 15x3) such that:
Ax <= b,
x1, x2, x3 >= 0,
A = | 1 2 3/2|, b = |12000|, c = |11|
|2/3 2/3 1 | | 4600| |16|
|1/2 1/3 1/2| | 2400| |15|
Source: http://college.cengage.com/mathematics/larson/elementary_linear/4e/shared/downloads/c09s3.pdf, Example 4
'''
self.assertDictEqual(
{
'x_1': Fraction(600),
'x_2': Fraction(5100),
'x_3': Fraction(800),
's_1': Fraction(0),
's_2': Fraction(0),
's_3': Fraction(0),
'z': Fraction(100200)
},
SimplexSolver().run_simplex([[1, 2, Fraction(
3, 2)], [Fraction(2, 3), Fraction(2, 3), 1
], [Fraction(1, 2),
Fraction(1, 3),
Fraction(1, 2)]], [12000, 4600, 2400],
[11, 16, 15]))
def test_max_feasible6(self):
''' Find optimal solution to max(11x1 + 16x2 + 15x3) such that:
Ax <= b,
x1, x2, x3 >= 0,
A = |20 6 3|, b = |182|, c = |100000|
| 0 1 0| | 10| | 40000|
|-1 -1 1| | 0| | 18000|
|-9 1 1| | 0|
Source: http://college.cengage.com/mathematics/larson/elementary_linear/4e/shared/downloads/c09s3.pdf, Example 5
'''
self.assertDictEqual(
{
'x_1': Fraction(4),
'x_2': Fraction(10),
'x_3': Fraction(14),
's_1': Fraction(0),
's_2': Fraction(0),
's_3': Fraction(0),
's_4': Fraction(12),
'z': Fraction(1052000)
},
SimplexSolver().run_simplex(
[[20, 6, 3], [0, 1, 0], [-1, -1, 1], [-9, 1, 1]],
[182, 10, 0, 0], [100000, 40000, 18000]))
def test_min_feasible3(self):
''' Find optimal solution to min(20000x1 + 25000x2) such that:
Ax >= b,
x1, x2 >= 0,
A = |400 300|, b = |25000|, c = |20000|
|300 400| |27000| |25000|
|200 500| |30000|
Source: http://college.cengage.com/mathematics/larson/elementary_linear/4e/shared/downloads/c09s4.pdf, Example 3
'''
self.assertDictEqual({'x_1': Fraction(25),
'x_2': Fraction(50),
's_1': Fraction(0),
's_2': Fraction(0),
'y_1': Fraction(250,7),
'y_2': Fraction(0),
'y_3': Fraction(200, 7),
'z': Fraction(1750000)},
SimplexSolver().run_simplex([[400,300],
[300,400],
[200,500]],
[25000,
27000,
30000],
[20000,25000],
prob='min'))
def test_max_feasible1(self):
''' Find optimal solution to max(x1 + x2) such that:
Ax <= b,
x1, x2 >= 0,
A = |2 1|, b = |4|, c = |1|
|1 2| |3| |1|
Source: http://mat.gsia.cmu.edu/classes/QUANT/NOTES/chap7.pdf, Example 7.2.1
'''
self.assertDictEqual(
{
'x_1': Fraction(5, 3),
'x_2': Fraction(2, 3),
's_1': Fraction(0),
's_2': Fraction(0),
'z': Fraction(7, 3)
},
SimplexSolver().run_simplex([[2, 1], [1, 2]], [4, 3], [1, 1]))
def test_max_feasible2(self):
''' Find optimal solution to max(4x1 + 6x2) such that:
Ax <= b,
x1, x2 >= 0,
A = |-1 1|, b = |11|, c = |4|
| 1 1| |27| |6|
| 2 5| |90|
Source: http://college.cengage.com/mathematics/larson/elementary_linear/4e/shared/downloads/c09s3.pdf, Example 1
'''
self.assertDictEqual(
{
'x_1': Fraction(15),
'x_2': Fraction(12),
's_1': Fraction(14),
's_2': Fraction(0),
's_3': Fraction(0),
'z': Fraction(132)
},
SimplexSolver().run_simplex([[-1, 1], [1, 1], [2, 5]],
[11, 27, 90], [4, 6]))
def test_min_feasible1(self):
''' Find optimal solution to min(3x1 + 2x2) such that:
Ax >= b,
x1, x2 >= 0,
A = |2, 1|, b = |6|, c = |3|
|1, 1| |4| |2|
Source: http://college.cengage.com/mathematics/larson/elementary_linear/4e/shared/downloads/c09s4.pdf, Example 1
'''
self.assertDictEqual(
{
'x_1': Fraction(2),
'x_2': Fraction(2),
's_1': Fraction(0),
's_2': Fraction(0),
'y_1': Fraction(1),
'y_2': Fraction(1),
'z': Fraction(10)
},
SimplexSolver().run_simplex([[2, 1], [1, 1]], [6, 4], [3, 2],
prob='min'))
def test_max_feasible4(self):
''' Find optimal solution to max(2x1 - x2 + 2x3) such that:
Ax <= b,
x1, x2, x3 >= 0,
A = |4 1 1|, b = |30|, c = |3|
|2 3 1| |60| |2|
|1 2 3| |40| |1|
Source: http://college.cengage.com/mathematics/larson/elementary_linear/4e/shared/downloads/c09s3.pdf, Example 3
'''
self.assertDictEqual(
{
'x_1': Fraction(3),
'x_2': Fraction(18),
'x_3': Fraction(0),
's_1': Fraction(0),
's_2': Fraction(0),
's_3': Fraction(1),
'z': Fraction(45)
},
SimplexSolver().run_simplex([[4, 1, 1], [2, 3, 1], [1, 2, 3]],
[30, 60, 40], [3, 2, 1]))
def test_max_feasible3(self):
''' Find optimal solution to max(2x1 - x2 + 2x3) such that:
Ax <= b,
x1, x2 >= 0,
A = |2 1 0|, b = |10|, c = | 2|
|1 2 -2| |20| |-1|
|0 1 2| | 5| | 2|
Source: http://college.cengage.com/mathematics/larson/elementary_linear/4e/shared/downloads/c09s3.pdf, Example 2
'''
self.assertDictEqual(
{
'x_1': Fraction(5),
'x_2': Fraction(0),
'x_3': Fraction(5, 2),
's_1': Fraction(0),
's_2': Fraction(20),
's_3': Fraction(0),
'z': Fraction(15)
},
SimplexSolver().run_simplex([[2, 1, 0], [1, 2, -2], [0, 1, 2]],
[10, 20, 5], [2, -1, 2]))