2.27

import numpy as np
import matplotlib.pyplot as plt
import random

def plot(x1, x2, point_x1, point_x2, color='blue', label=r'$x_1 + 3x_2 ≥ 3$', upper=1):
    plt.plot(x1, x2, c=color)
    plt.scatter(point_x1, point_x2, marker='o', c=color)
    if upper == 1:
        plt.fill_between(x1, x2, max(x2), color=color, alpha=0.15, label=label)
    else:
        plt.fill_between(x1, x2, min(x2), color=color, alpha=0.15, label=label)

colors = ['blue', 'green', 'red', 'cyan', 'magenta', 'yellow', 'black', 'white', 'orange', 'purple', 'pink', 'brown', 'gray']

scale = 10

x1 = np.linspace(-100, 100, 1000)

plt.figure(figsize=(10, 5))
plt.title(r'$L = 3x_1 + 0x_2 + 4\rightarrow max$')

plt.plot(np.linspace(-100, 100, 1000), np.array([0 for i in range(1000)]), c='black')
plt.plot(np.array([0 for i in range(1000)]), np.linspace(-100, 100, 1000), c='black')

random_x1_f1 = random.uniform(-2, scale)
random_x2_f1 = random.uniform(-2, scale)
print(f"Пробна точка: ({round(random_x1_f1, 2)}, {round(random_x2_f1, 2)})")
def f1(x1):
    return 4 + 2*x1

x2 = f1(x1)
print(f'(-2*{round(random_x1_f1, 2)}) + ({round(random_x2_f1, 2)}) < 4')
print(f'{round(-2*random_x1_f1 + random_x2_f1, 2)} < 4')
print(f'{-2*random_x1_f1 + random_x2_f1 < 4}\n')
if -2*random_x1_f1 + random_x2_f1 < 4:
    upper = 0
else:
    if random_x2_f1 > f1(random_x1_f1):
        upper = 0
    else:
        upper = 1
plt.scatter(random_x1_f1, random_x2_f1, c=colors[0])
plot(x1, x2, np.array([0, 2]), np.array([4, 8]), colors[0], label=r'$-2x_1 + x_2 < 4$', upper=upper)

plt.grid()
plt.legend()
plt.xlim(-3, scale)
plt.ylim(-3, scale)
plt.show()









plt.figure(figsize=(10, 5))
plt.title(r'$L = 3x_1 + 0x_2 + 4\rightarrow max$')

plt.plot(np.linspace(-100, 100, 1000), np.array([0 for i in range(1000)]), c='black')
plt.plot(np.array([0 for i in range(1000)]), np.linspace(-100, 100, 1000), c='black')

print(f"Пробна точка: ({round(random_x1_f1, 2)}, {round(random_x2_f1, 2)})")
def f1(x1):
    return 4 + 2*x1

x2 = f1(x1)
print(f'(-2*{round(random_x1_f1, 2)}) + ({round(random_x2_f1, 2)}) < 4')
print(f'{round(-2*random_x1_f1 + random_x2_f1, 2)} < 4')
print(f'{-2*random_x1_f1 + random_x2_f1 < 4}\n')
if -2*random_x1_f1 + random_x2_f1 < 4:
    upper = 0
else:
    if random_x2_f1 > f1(random_x1_f1):
        upper = 0
    else:
        upper = 1
plt.scatter(random_x1_f1, random_x2_f1, c=colors[0])
plot(x1, x2, np.array([0, 2]), np.array([4, 8]), colors[0], label=r'$-2x_1 + x_2 < 4$', upper=upper)


random_x1_f2 = random.uniform(-2, scale)
random_x2_f2 = random.uniform(-2, scale)
print(f"Пробна точка: ({round(random_x1_f2, 2)}, {round(random_x2_f2, 2)})")
def f2(x1):
    return (-1 + x1) / 2
x2 = f2(x1)
print(f'(-{round(random_x1_f2, 2)}) + (2*{round(random_x2_f2, 2)}) > -1')
print(f'{round(-random_x1_f2 + 2*random_x2_f2, 2)} > -1')
print(f'{-random_x1_f2 + 2*random_x2_f2 > -1}\n')
if -random_x1_f2 + 2*random_x2_f2 > -1:
    upper = 1
else:
    if random_x2_f2 < f2(random_x1_f2):
        upper = 1
    else:
        upper = 0
plt.scatter(random_x1_f2, random_x2_f2, c=colors[1])
plot(x1, x2, np.array([1, 3]), np.array([0, 1]), colors[1], label=r'$-x_1 + 2x_2 > -1$', upper=upper)

plt.grid()
plt.legend()
plt.xlim(-3, scale)
plt.ylim(-3, scale)
plt.show()





plt.figure(figsize=(10, 5))
plt.title(r'$L = 3x_1 + 0x_2 + 4\rightarrow max$')
plt.plot(np.linspace(-100, 100, 1000), np.array([0 for i in range(1000)]), c='black')
plt.plot(np.array([0 for i in range(1000)]), np.linspace(-100, 100, 1000), c='black')


print(f"Пробна точка: ({round(random_x1_f1, 2)}, {round(random_x2_f1, 2)})")
def f1(x1):
    return 4 + 2*x1

x2 = f1(x1)
print(f'(-2*{round(random_x1_f1, 2)}) + ({round(random_x2_f1, 2)}) < 4')
print(f'{round(-2*random_x1_f1 + random_x2_f1, 2)} < 4')
print(f'{-2*random_x1_f1 + random_x2_f1 < 4}\n')
if -2*random_x1_f1 + random_x2_f1 < 4:
    upper = 0
else:
    if random_x2_f1 > f1(random_x1_f1):
        upper = 0
    else:
        upper = 1
plt.scatter(random_x1_f1, random_x2_f1, c=colors[0])
plot(x1, x2, np.array([0, 2]), np.array([4, 8]), colors[0], label=r'$-2x_1 + x_2 < 4$', upper=upper)


print(f"Пробна точка: ({round(random_x1_f2, 2)}, {round(random_x2_f2, 2)})")
def f2(x1):
    return (-1 + x1) / 2
x2 = f2(x1)
print(f'(-{round(random_x1_f2, 2)}) + (2*{round(random_x2_f2, 2)}) > -1')
print(f'{round(-random_x1_f2 + 2*random_x2_f2, 2)} > -1')
print(f'{-random_x1_f2 + 2*random_x2_f2 > -1}\n')
if -random_x1_f2 + 2*random_x2_f2 > -1:
    upper = 1
else:
    if random_x2_f2 < f2(random_x1_f2):
        upper = 1
    else:
        upper = 0
plt.scatter(random_x1_f2, random_x2_f2, c=colors[1])
plot(x1, x2, np.array([1, 3]), np.array([0, 1]), colors[1], label=r'$-x_1 + 2x_2 > -1$', upper=upper)




x2 = np.copy(x1)
plt.axvline(x=-4/3, lw=2, color='black')
plt.scatter(np.array([-4/3, -4/3]), np.array([4, 0]), c='black')

plt.annotate('Вектор нормалі', xy=(3, 0), xycoords='data', xytext=(-3.3, 0.1), textcoords='data', arrowprops=dict(facecolor='black'))

plt.scatter(100, 1000, c='red', edgecolors='black', s=50, label=r'$L_{max} \rightarrow \infty$')
plt.grid()
plt.legend()
plt.xlim(-3, scale)
plt.ylim(-3, scale)
plt.show()