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import matplotlib.pyplot as plt
import numpy as np

# Define the range of x and y values
x_vals = np.linspace(0, 50, 400)
y_vals = np.linspace(0, 50, 400)

# Constraints
y1 = (100 - x_vals) / 5          # Line for 1x + 5y = 100
y2 = (66 - 3 * x_vals) / 2       # Line for 3x + 2y = 66
y3 = (136 - 8 * x_vals) / 2      # Line for 8x + 2y = 136

# Profit lines
P34 = (34 - 2 * x_vals) / 3      # Line for P = 34
P60 = (60 - 2 * x_vals) / 3      # Line for P = 60
P64 = (64 - 2 * x_vals) / 3      # Line for P = 64
P74 = (74 - 2 * x_vals) / 3      # Line for P = 74
P80 = (80 - 2 * x_vals) / 3      # Line for P = 80

# Plot the constraints
plt.figure(figsize=(10, 8))
plt.plot(x_vals, y1, label='1x + 5y = 100', color='blue')
plt.plot(x_vals, y2, label='3x + 2y = 66', color='green')
plt.plot(x_vals, y3, label='8x + 2y = 136', color='red')

# Plot the profit lines
plt.plot(x_vals, P34, '--', label='P = 34$', color='purple')
plt.plot(x_vals, P60, '--', label='P = 60$', color='orange')
plt.plot(x_vals, P64, '--', label='P = 64$', color='brown')
plt.plot(x_vals, P74, '--', label='P = 74$', color='pink')
plt.plot(x_vals, P80, '--', label='P = 80$', color='cyan')

# Set plot limits
plt.xlim(0, 50)
plt.ylim(0, 50)

# Add labels and legend
plt.xlabel('x (Crêpes)')
plt.ylabel('y (Cakes)')
plt.title('Constraints and Profit Lines')
plt.legend(loc='upper right')
plt.grid()

# Show the plot
plt.show()