Solving a linear programming problem with PuLP



In [1]:

    
import pulp

Objective function

$$z(max) = 5x_1 + 4x_2$$

Constraints:

$C_1 = x_1 + x_2 \leq 5$
$C_2 = 10*x_1 + 6*x_2 \leq 45$
$x_1,x_2 \geq 0$



In [2]:

    
z = pulp.LpProblem('problem x', pulp.LpMaximize)
x1 = pulp.LpVariable('x1', lowBound=0)
x2 = pulp.LpVariable('x2', lowBound=0)



In [3]:

    
z += 5*x1 + 4*x2



In [4]:

    
z += 1*x1 + 1*x2 <= 5
z += 10*x1 + 6*x2 <= 45



In [5]:

    
z









    Out[5]:





problem x:
MAXIMIZE
5*x1 + 4*x2 + 0
SUBJECT TO
_C1: x1 + x2 <= 5

_C2: 10 x1 + 6 x2 <= 45

VARIABLES
x1 Continuous
x2 Continuous



In [6]:

    
pulp.LpStatus[z.solve()]









    Out[6]:





'Optimal'



In [7]:

    
pulp.value(x1), pulp.value(x1), pulp.value(z.objective)









    Out[7]:





(3.75, 3.75, 23.75)