Minimise and Maximise `Z=x+2y`
Subject to `x+2yge100,2x-yle0,2x+yle200,x,yge0`.

Explanation

To solve the problem of minimizing and maximizing the function \( Z = x + 2y \) subject to the given constraints, we will follow these steps:

### Step 1: Write down the constraints
We have the following constraints:
1. \( x + 2y \geq 100 \)
2. \( 2x - y \geq 0 \)
3. \( 2x + y \geq 200 \)
4. \( x \geq 0 \)
...