Solve_linear_system_glpk.py

import glpk            # Import the GLPK module                                                                                                                                         

lp = glpk.LPX()              # Create empty problem instance                                                                                                                            
lp.name = 'optimization'     # Assign symbolic name to problem                                                                                                                          
#lp.obj.maximize = True      # Set this as a maximization problem                                                                                                                       
lp.obj.maximize = False      # Set this as a minimization problem                                                                                                                       

lp.rows.add(3)         # Append three rows to this instance                                                                                                                             
for r in lp.rows:      # Iterate over all rows                                                                                                                                          
    r.name = chr(ord('p')+r.index) # Name them p, q, and r                                                                                                                              
    print(r.name)

#lp.rows[0].bounds = None, 100.0  # Set bound -inf < p <= 100                                                                                                                           
#lp.rows[1].bounds = None, 600.0  # Set bound -inf < q <= 600                                                                                                                           
#lp.rows[2].bounds = None, 300.0  # Set bound -inf < r <= 300                                                                                                                           

lp.rows[0].bounds = 100, 100.0  # Set equality p = 100                                                                                                                                  
lp.rows[1].bounds = 600, 600.0  # Set equality q = 600                                                                                                                                  
lp.rows[2].bounds = 300, 300.0  # Set equality r = 300                                                                                                                                  


lp.cols.add(3)         # Append three columns (incognitae) to this instance                                                                                                             
for c in lp.cols:      # Iterate over all columns                                                                                                                                       
    c.name = 'x%d' % c.index # Name them x0, x1, x2,...                                                                                                                                 
    c.bounds = 0.0, None     # Set bound 0 <= xi < inf                                                                                                                                  
    print(c.name)

##Define the problem here                                                                                                                                                               
lp.obj[:] = [ 10.0, 6.0, 4.0 ]   # Set objective coefficients                                                                                                                           
lp.matrix = [ 1.0, 1.0, 1.0,     # Set nonzero entries of the                                                                                                                           
              10.0, 4.0, 5.0,     #   constraint matrix.  (In this                                                                                                                      
              2.0, 2.0, 6.0 ]    #   case, all are non-zero.)                                                                                                                           
lp.simplex()           # Solve this LP with the simplex method                                                                                                                          
print 'Z = %g;' % lp.obj.value,  # Retrieve and print obj func value                                                                                                                    
print '; '.join('%s = %g' % (c.name, c.primal) for c in lp.cols)
# Print struct variable names and primal values