Consider the linear program: $$ \left.\begin{array}{rrcl} \max & -2x+y \\ \text {s.t.:} & & & \\ & -x + y \leq 1 \text{ (Constraint 1)}\\ & x+y \geq 0 \text{ (Constraint 2)} \\ & x, y \geq 0 \text{ (Non-negativity)} \\ \end{array}\right\} $$
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%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
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x = [0, 4, 4, 3, 0]
y = [0, 0, 4, 4, 1]
plt.fill(x,y)
plt.show()
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fig = plt.figure()
ax = plt.axes()
x = np.linspace(0, 2, 500)
ax.plot(x, x+1, linestyle='--', label='y = x+1');
ax.plot(x, -x, linestyle='--')
ax.plot(x, 0*x, linestyle='--')
ax.plot(x, 2*x+1, linestyle='-')
plt.fill_between(x, x+1, 0*x, color='grey', alpha='0.5')
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