Maximize Optimization using Scipy

Question

I'm trying to solve this linear programming function with the restraints shown below, the answer for x1 and x2 should be 2 and 6 respectively, and the value of the objective function should be equal to 36. The code that I wrote gives me as answers 4 and 3. What may I be doing wrong? Function to maximize z=3*x1 + 5*x2. Restraints are x1 <= 4;2*x2 <=12; 3*x1 + 2*x2 <= 18; x1>=0;x2>=0.

import numpy as np
from scipy.optimize import minimize
def objective(x, sign=1.0):
    x1 = x[0]
    x2 = x[1]
    return sign*((3*x1) + (5*x2))
def constraint1(x, sign=1.0):
    return sign*(3*x[0] +2*x[1]- 18.0)
x0=[0,0]

b1 = (0,4)
b2 = (0,12)
bnds= (b1,b2)
con1 = {'type': 'ineq', 'fun': constraint1}

cons = [con1]
sol = minimize (objective,x0,method='SLSQP',bounds=bnds,constraints=cons)

print(sol)

Answer 1

Your code has the following issues:

• The way you are passing your objective to minimize results in a minimization rather than a maximization of the objective. If you want to maximize objective with minimize you should set the sign parameter to -1. See the maximization example in scipy documentation.
• minimize assumes that the value returned by a constraint function is greater than zero. Therefore, the way you have written your constraint implies that 3*x1 + 2*x2 - 18.0 >=0, whereas the actual constraint employs <=.
• The upper bound in b2 does not correspond to the bound implied by the constraint 2*x2 <= 12.