import numpy as np

# Puzzle:
# Consider a portfolio of N assets with known expected returns (mu) and a covariance matrix (cov_matrix).
# You have a target return (target_return) that you want to achieve.
# Find the optimal weights (w) for the assets to achieve the target return, subject to the constraint
# that the sum of weights must be equal to 1.

# Define the parameters
N = 3  # Number of assets
target_return = 0.05  # Target portfolio return

# Example expected returns and covariance matrix (replace with real data)
mu = np.array([0.03, 0.05, 0.08])
cov_matrix = np.array([[0.0004, 0.0002, 0.0001],
                       [0.0002, 0.0003, 0.00015],
                       [0.0001, 0.00015, 0.00025]])

# Define the objective function for the optimization problem
def objective(weights, mu):
    return -np.dot(weights, mu)

# Define the constraint for the weights summing to 1
def constraint(weights):
    return np.sum(weights) - 1

# Set up the optimization problem
initial_weights = np.ones(N) / N  # Initial equal weights for each asset
constraints = ({'type': 'eq', 'fun': constraint})
bounds = tuple((0, 1) for asset in range(N))

# Solve the optimization problem
from scipy.optimize import minimize
result = minimize(objective, initial_weights, args=(mu,), method='SLSQP', bounds=bounds, constraints=constraints)

# Print the results
optimal_weights = result.x
optimal_portfolio_return = -result.fun
print("Optimal Weights:", optimal_weights)
print("Optimal Portfolio Return:", optimal_portfolio_return)