Solving an integer linear programming problem with PuLP



In [1]:

    
import pulp

Objective function

$$z(max) = 7x_1 + 6x_2$$

Constraints:

$C_1 = 2x_1 + 3x_2 \leq 12$
$C_2 = 6x_1 + 5x_2 \leq 30$
$x_1,x_2 \geq 0$
$x_1, x_2 \space must \space be \space Integers$



In [2]:

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



In [3]:

    
z += 7*x1 + 6*x2



In [4]:

    
z += 2*x1 + 3*x2 <= 12
z += 6*x1 + 5*x2 <= 30



In [5]:

    
pulp.LpStatus[z.solve()]









    Out[5]:





'Optimal'



In [6]:

    
pulp.value(x1), pulp.value(x2), pulp.value(z.objective)









    Out[6]:





(5.0, 0.0, 35.0)