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com2014-template/Workshop - 3 (LP).ipynb

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Make sure you run this at the begining

In [1]:
import numpy as np
np.set_printoptions(suppress=True)
from scipy.optimize import linprog

Feasible Example

\begin{align} \max f=4x_1+x_2 \\ \text{s.t.} -x_1 + 2x_2 &\leq 4 \\ 2x_1 + 3x_2 &\leq 12 \\ x_1 - x_2 &\leq 3 \\ \text{and } x_1, x_2 \geq 0 \end{align}
In [2]:
c = [-4, -1, 0, 0, 0]
A = [[-1, 2, 0, 0, 0], [2, 3, 0, 0, 0], [1, -1, 0, 0, 0]]
b = [4, 12, 3]

x0_bounds = (0, None)
x1_bounds = (0, None)
x2_bounds = (None, None)
x3_bounds = (None, None)
x4_bounds = (None, None)
In [3]:
res = linprog(c, A_ub=A, b_ub=b, bounds=[x0_bounds, x1_bounds, x2_bounds, x3_bounds, x4_bounds])

print(res)

     con: array([], dtype=float64)
     fun: -17.999999976555795
 message: 'Optimization terminated successfully.'
     nit: 4
   slack: array([5.8       , 0.00000002, 0.        ])
  status: 0
 success: True
       x: array([4.19999999, 1.2       , 0.        , 0.        , 0.        ])
In [ ]:

Infeasible Example

\begin{align} \min f = x_1 - 2x_2 + 3x_3 \\ s.t. -2x_1 + x_2 + 3x_3 & = 2 \\ 3x_1 + 3x_2 + 4x_3 & = 1 \\ \end{align}
In [4]:
c = [-1, 2, -3]
A = [[-2, 1, 3], [3, 3, 4]]
b = [2, 1]

x0_bounds = (0, None)
x1_bounds = (0, None)
x2_bounds = (0, None)
In [5]:
res = linprog(c, A_eq=A, b_eq=b, bounds=[x0_bounds, x1_bounds, x2_bounds,])

print(res)

     con: array([ 0.        , -4.56053464])
     fun: -0.6099904044751114
 message: 'The algorithm terminated successfully and determined that the problem is infeasible.'
     nit: 4
   slack: array([], dtype=float64)
  status: 2
 success: False
       x: array([0.2893146 , 0.75265113, 0.60865936])
In [ ]:

Assignment

\begin{align} \min f = 3x_1 - x_2 \\ s.t. 2x_1 + x_2 & \geq 2 \\ x_1 + 3x_2 & \leq 3 \\ x_2 & \leq 4 \\ \text{and } x_1, x_2 \geq 0 \end{align}
In [6]:
c = [-3, 1]
A = [[-2, -1], [1, 3], [0, 1]]
b = [-2, 3, 4]

x0_bounds = (0, None)
x1_bounds = (0, None)
In [7]:
res = linprog(c, A_ub=A, b_ub=b, bounds=[x0_bounds, x1_bounds])

print(res)

     con: array([], dtype=float64)
     fun: -8.999999998556428
 message: 'Optimization terminated successfully.'
     nit: 4
   slack: array([4., 0., 4.])
  status: 0
 success: True
       x: array([3., 0.])
In [ ]:
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