def greedy_optimization(TOTAL_BUDGET, alphas, betas, num_iterations=1_000):
    # Initialize the budget allocation and the best objective value
    google_budget = facebook_budget = twitter_budget = TOTAL_BUDGET / 3
    obj = alphas[0] + betas[0] * np.log(google_budget) + alphas[1] + betas[1] * np.log(facebook_budget) + alphas[2] + betas[2] * np.log(twitter_budget)

    for _ in range(num_iterations):
        # Generate a new random allocation
        random_allocation = np.random.dirichlet(np.ones(3)) * TOTAL_BUDGET
        google_budget_new, facebook_budget_new, twitter_budget_new = random_allocation

        # Calculate the new objective value
        new_obj = alphas[0] + betas[0] * np.log(google_budget_new) + alphas[1] + betas[1] * np.log(facebook_budget_new) + alphas[2] + betas[2] * np.log(twitter_budget_new)

        # If the new allocation improves the objective value, keep it
        if new_obj > obj:
            google_budget, facebook_budget, twitter_budget = google_budget_new, facebook_budget_new, twitter_budget_new
            obj = new_obj

    # Return the best allocation and the corresponding objective value
    return (google_budget, facebook_budget, twitter_budget), objp