import numpy as np from scipy.optimize import minimize

Define the cost function for power generation

def cost_function(x): # Assuming a linear cost function: C = a * P + b a = 0.1 # Cost coefficient b = 10 # Cost constant return a * x + b

Define the objective function to be minimized

def objective_function(x): return np.sum(cost_function(x))

Define the power demand constraint

def demand_constraint(x): return np.sum(x) - demand

Define the power generation limit constraint

def limit_constraint(x): return max(x) - max_generation

Define the system constraints

constraints = [ {'type': 'eq', 'fun': demand_constraint}, {'type': 'ineq', 'fun': limit_constraint} ]

Define the initial guess for power generation

x0 = np.array([0.0])

Define the power demand and maximum power generation

demand = 100.0 max_generation = 150.0

Solve the optimization problem

solution = minimize(objective_function, x0, constraints=constraints) x_optimal = solution.x

Print the optimal power generation and total cost

print("Optimal power generation:", x_optimal[0]) print("Total cost of power generation:", objective_function(x_optimal))