If you start the plot in point (0, 0), and therefore do not need to consider the area of the polygon not in the first quadrant, then this should do the trick in this particular situation:

```
import matplotlib.pyplot as plt
import numpy as np
x = np.arange(0,10,0.1)
# The lines to plot
y1 = 4 - 2*x
y2 = 3 - 0.5*x
y3 = 1 -x
# The upper edge of polygon (min of lines y1 & y2)
y4 = np.minimum(y1, y2)
# Set y-limit, making neg y-values not show in plot
plt.ylim(0, 5)
# Plotting of lines
plt.plot(x, y1,
x, y2,
x, y3)
# Filling between line y3 and line y4
plt.fill_between(x, y3, y4, color="grey", alpha="0.5")
plt.show()
```