glpk_linear_programming_maximize_with_simplex_solver.py

1import glpk
2
3# Create a new problem instance
4lp = glpk.LPX()
5
6# Set the problem name and optimization direction (maximize)
7lp.name = 'sample'
8lp.obj.maximize = True
9
10# Add rows (constraints) to the problem
11lp.rows.add(3)
12for r in lp.rows:
13    r.name = f'p{r.index}'
14
15# Set constraint bounds (lb, ub)
16lp.rows[0].bounds = None, 100.0
17lp.rows[1].bounds = None, 600.0
18lp.rows[2].bounds = None, 300.0
19
20# Add columns (variables) to the problem
21lp.cols.add(3)
22for c in lp.cols:
23    c.name = f'x{c.index}'
24    c.bounds = 0.0, None  # Non-negative variables
25
26# Set objective function coefficients
27lp.obj[:] = [10.0, 6.0, 4.0]
28
29# Set the constraint matrix (coefficients for the constraints)
30lp.matrix = [
31    1.0, 1.0, 1.0,  # Row 0 coefficients
32    10.0, 4.0, 5.0, # Row 1 coefficients
33    2.0, 2.0, 6.0   # Row 2 coefficients
34]
35
36# Solve the linear programming problem using the simplex method
37lp.simplex()
38
39# Print the results
40print(f'Objective value: {lp.obj.value}')
41for c in lp.cols:
42    print(f'{c.name} = {c.value}')