Untitled

import numpy as np
from scipy.optimize import minimize

def objective(x):
    # Calculate the objective function value
    f = x[0] * x[3] * (x[0] + x[1] + x[2]) + x[2]
    return f

def constraint1(x):
    # Calculate the constraint function value
    return x[0] * x[1] * x[2] * x[3] - 25.0

def constraint2(x):
    # Calculate the constraint function value
    sum_sq = 40.0
    for i in range(4):
        sum_sq = sum_sq - x[i]**2
    return sum_sq

# Initialize the design variables
x0 = [1, 5, 5, 1]

# Set the bounds for the design variables
b = (1.0, 5.0)
bnds = (b, b, b, b)

# Set the constraints
con1 = {"type": "ineq", "fun": constraint1}
con2 = {"type": "eq", "fun": constraint2}
cons = [con1, con2]

# Run the optimization
solution = minimize(objective, x0, method="SLSQP", bounds=bnds, constraints=cons)

# Print the results
print(f"Optimal design variables: {solution.x}")
print(f"Objective function value: {solution.fun}")