Minimize ` z = x + 2y`, subject to ` x + 2y ge 50 ` , ` 2x - y le 0 , 2x + y le 100, x , y ge 0 . `

Explanation

To solve the linear programming problem of minimizing \( z = x + 2y \) subject to the constraints, we will follow these steps:

### Step 1: Write down the constraints
The constraints given are:
1. \( x + 2y \geq 50 \)
2. \( 2x - y \leq 0 \) (or equivalently \( y \geq 2x \))
3. \( 2x + y \leq 100 \)
4. \( x \geq 0 \)
...