python Linear Programming visualization the process

Author: xlisp

linear_programming_visualization.png

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+## python Linear Programming visualization the process
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+# Define the constraints
+x1 = np.linspace(0, 10, 400)
+
+# Constraint 1: x1 + x2 <= 5
+x2_1 = 5 - x1
+
+# Constraint 2: 2x1 + x2 <= 8
+x2_2 = 8 - 2*x1
+
+# Feasibility boundary for x2 >= 0
+x2_0 = np.maximum(0, np.minimum(x2_1, x2_2))
+
+# Plot the constraints
+plt.figure(figsize=(8, 8))
+
+# Plot the lines representing the constraints
+plt.plot(x1, x2_1, label=r'$x_1 + x_2 \leq 5$')
+plt.plot(x1, x2_2, label=r'$2x_1 + x_2 \leq 8$')
+
+# Shade the feasible region
+plt.fill_between(x1, 0, x2_0, where=(x2_0 >= 0), color='lightgrey', label='Feasible Region')
+
+# Mark corner points
+corner_points = [(0, 0), (0, 5), (4, 0), (2, 3)]
+for point in corner_points:
+    plt.scatter(*point, color='red')
+    plt.text(point[0] + 0.1, point[1] - 0.2, f'({point[0]}, {point[1]})', color='black')
+
+# Labels and title
+plt.xlim(0, 6)
+plt.ylim(0, 6)
+plt.xlabel('$x_1$')
+plt.ylabel('$x_2$')
+plt.title('Linear Programming Problem Visualization')
+plt.legend()
+
+# Show the plot
+plt.grid(True)
+plt.show()
+