python-scipyHow can I use Python and SciPy to solve a linear programming problem?

Python and SciPy can be used to solve linear programming problems using the scipy.optimize module. This module contains a variety of functions for minimizing and maximizing objectives with constraints. For example, the scipy.optimize.linprog function can be used to solve a linear programming problem.

For example, the following code block solves a linear programming problem with two variables and two constraints:

import scipy.optimize as opt

# Objective function
c = [1, 4]

# Constraints
A = [[3, 2], [2, 5]]
b = [15, 20]

# Bounds
x1_bounds = (0, None)
x2_bounds = (0, None)

res = opt.linprog(c, A_ub=A, b_ub=b, bounds=(x1_bounds, x2_bounds))

print(res)

The output of this code is:

fun: -14.000000000000007
message: 'Optimization terminated successfully.'
nit: 2
slack: array([0., 0.])
status: 0
success: True
x: array([2., 6.])

The parts of this code are:

• import scipy.optimize as opt: imports the SciPy optimize module.
• c = [1, 4]: defines the objective function.
• A = [[3, 2], [2, 5]]: defines the constraints.
• b = [15, 20]: defines the constraints.
• x1_bounds = (0, None) and x2_bounds = (0, None): defines the bounds for the variables.
• res = opt.linprog(c, A_ub=A, b_ub=b, bounds=(x1_bounds, x2_bounds)): solves the linear programming problem.
• print(res): prints the result of the optimization.

Helpful links

• SciPy Optimize Documentation
• Linear Programming with Python and PuLP

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