对应实现图解代码参考：
import numpy as np
import matplotlib.pyplot as plt
import matplotlib as mpl# ========== 修正字体配置（适配Mac系统） ==========
# 方案1：使用Mac自带的支持下标的中文字体
plt.rcParams['font.family'] = ['Arial Unicode MS', 'SimHei', 'DejaVu Sans']
plt.rcParams['axes.unicode_minus'] = False
# 方案2：禁用matplotlib的下标渲染，改用普通括号标注（备选）
mpl.rcParams['mathtext.fontset'] = 'custom'
mpl.rcParams['mathtext.rm'] = 'Arial'
mpl.rcParams['mathtext.it'] = 'Arial:italic'
mpl.rcParams['mathtext.bf'] = 'Arial:bold'# 1. 定义绘图范围
x1 = np.linspace(-1, 7, 500) # x1的取值范围
x2 = np.linspace(-1, 5, 500) # x2的取值范围
X1, X2 = np.meshgrid(x1, x2)# 2. 定义约束条件
constraint1 = 0.5 * X1 + X2 <= 4 # 0.5x1 + x2 ≤ 4
constraint2 = 3 * X1 + X2 <= 15 # 3x1 + x2 ≤ 15
constraint3 = X1 + X2 >= 1 # x1 + x2 ≥ 1
constraint4 = X1 >= 0 # x1 ≥ 0
constraint5 = X2 >= 0 # x2 ≥ 0# 可行域：所有约束的交集
feasible_region = constraint1 & constraint2 & constraint3 & constraint4 & constraint5# 3. 定义目标函数 (x1-6)² + (x2-2)²
def objective_func(x1, x2):return (x1 - 6)**2 + (x2 - 2)**2# 4. 绘制图形
fig, ax = plt.subplots(figsize=(10, 8))# 绘制可行域（浅蓝色填充）
ax.contourf(X1, X2, feasible_region.astype(int), levels=[0, 1],colors=['white', 'lightblue'], alpha=0.5)# 绘制约束边界线（修正参数：分开color和linestyle）
ax.plot(x1, 4 - 0.5 * x1, 'r-', label=r'0.5x_1 + x_2 = 4') # 用LaTeX语法写下标
ax.plot(x1, 15 - 3 * x1, 'g-', label=r'3x_1 + x_2 = 15')
ax.plot(x1, 1 - x1, 'b-', label=r'x_1 + x_2 = 1')
ax.axvline(x=0, color='k', linestyle='--', alpha=0.5, label=r'x_1 = 0')
ax.axhline(y=0, color='k', linestyle='--', alpha=0.5, label=r'x_2 = 0')# 绘制目标函数等值线（同心圆）
z_values = objective_func(X1, X2)
contours = ax.contour(X1, X2, z_values, levels=[17, 25, 36, 49],colors='orange', linestyles='--')
ax.clabel(contours, inline=True, fontsize=8, fmt='z = %d')# 标记可行域顶点
vertices = [(0, 1), (0, 4), (2, 3), (5, 0), (1, 0)]
vertex_x = [v[0] for v in vertices]
vertex_y = [v[1] for v in vertices]
ax.scatter(vertex_x, vertex_y, color='red', s=50, zorder=5, label='可行域顶点')# 标记最优解 (2, 3)
ax.scatter(2, 3, color='darkred', s=80, marker='*', zorder=6, label='最优解 (2, 3)')
# 标记目标函数圆心 (6, 2)
ax.scatter(6, 2, color='purple', s=80, marker='o', zorder=6, label='目标函数圆心 (6, 2)')# 设置坐标轴和图例（改用LaTeX下标语法）
ax.set_xlabel(r'$x_1$', fontsize=12) # LaTeX语法渲染下标
ax.set_ylabel(r'$x_2$', fontsize=12)
ax.set_xlim(-1, 7)
ax.set_ylim(-1, 5)
ax.set_title('第4题 可行域与目标函数等值线图', fontsize=14)
ax.legend(loc='upper right')
ax.grid(True, alpha=0.3)plt.tight_layout()
plt.show()