Consider the Linear Programming Problem, where the objective function
\[
Z = x + 4y
\]
needs to be minimized subject to the following constraints:
\[
2x + y \geq 1000,
\]
\[
x + 2y \geq 800,
\]
\[
x \geq 0, \quad y \geq 0.
\]
Draw a neat graph of the feasible region and find the minimum value of $Z$.