35 lines
1.1 KiB
Python
35 lines
1.1 KiB
Python
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import numpy as np
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import matplotlib.pyplot as plt
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# Define the Langarian function
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def langarian(x1, x2, x3, lmbda):
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c1, c2, c3 = 10, 20, 25
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m1, m2, m3 = 10, 20, 25
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return (c1*x1 + c2*x2 + c3*x3) - lmbda*(m1*x1 + m2*x2 + m3*x3 - 100)
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# Define the constraint equation
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def constraint(x1, x2):
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m1, m2, m3 = 10, 20, 25
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return (100 - m1*x1 - m2*x2) / m3
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# Generate data for plotting
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x1_range = np.linspace(0, 10, 100)
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x2_range = np.linspace(0, 10, 100)
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X1, X2 = np.meshgrid(x1_range, x2_range)
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Z = langarian(X1, X2, constraint(X1, X2), 1)
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# Plot the Langarian function
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fig = plt.figure(figsize=(10, 6))
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ax = fig.add_subplot(111, projection='3d')
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ax.plot_surface(X1, X2, Z, cmap='viridis', alpha=0.8)
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ax.set_xlabel('x1')
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ax.set_ylabel('x2')
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ax.set_zlabel('L(x1, x2, x3)')
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# Plot the constraint equation
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x3_const = constraint(X1, X2)
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ax.plot_wireframe(X1, X2, x3_const, color='r', linewidth=1, linestyle='--', alpha=0.6)
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ax.scatter(0, 5, 0, color='r', marker='o') # Highlight the optimal point
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ax.text(0, 5, 0, "Optimal Point\n(0, 5, 0)", color='r')
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ax.set_title('Langarian Function and Constraint Equation')
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plt.show()
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