import matplotlib.pyplot as plt
import numpy as np
np.random.seed(0)

TOTAL_BUDGET = 100_000

# Alpha and beta constants
alphas = np.array([-9453.72, -8312.84, -7371.33])
betas = np.array([8256.21, 7764.20, 7953.36])

# Linearly spaced numbers
x = np.linspace(1, TOTAL_BUDGET, TOTAL_BUDGET)

# Plot the response curves
fig = plt.figure(figsize=(10, 5), dpi=300)
plt.plot(x, alphas[0] + betas[0] * np.log(x), color='red', label='Google Ads')
plt.plot(x, alphas[1] + betas[1] * np.log(x), color='blue', label='Facebook Ads')
plt.plot(x, alphas[2] + betas[2] * np.log(x), color='green', label='Twitter Ads')
plt.xlabel('Budget ($)')
plt.ylabel('Returns ($)') 
plt.legend()
plt.show()