Python Codes to solve LP Problem

There are several libraries available in Python for solving linear programming problems. Some of the most popular ones are:

1. script.optimize: 

Scipy is a python library that provides a wide range of optimization algorithms, including linprog which is used to solve linear programming problems. The function has the following format : scipy.optimize.linprog(c, A_ub=None, b_ub=None, A_eq=None, b_eq=None, bounds=None, method='simplex',callback=None,options=None)

2. cvxpy:

 A library for convex optimization, it can be used to model and solve linear programming problems. The library uses the standard form of linear programming problem which is min c'x subject to Ax <= b, x >= 0.

3. PuLP: 

A library for linear programming, it can be used to define and solve linear programming problems. It has an easy-to-use interface and supports both the primal and dual forms of the problem.

4. Gurobi: 

A commercial optimization solver, it can be used to solve linear programming problems and many other types of optimization problems. It is a powerful solver and is widely used in industry and research.

Here's an example of how to use the scipy.optimize.linprog function to solve a simple linear programming problem:

This code defines a linear programming problem with objective function coefficients c, constraints A and b, and bounds for the variables. The function then solves the problem using the simplex method and prints the results.

from scipy.optimize import linprog 
# objective function coefficients
c = [-1, 4] 
# constraints 
A = [[-3, 1], [1, 2]] 
b = [6, 4] 
# bounds 
x0_bounds = (None, None)
x1_bounds = (0, None) 
# solve 
res = linprog(c, A_ub=A, b_ub=b, bounds=[x0_bounds, x1_bounds], method='simplex')

# print results 
print(res)