Maximize `Z = x + 2y` subject to:
`2x + y ge 3, x + 2y ge 6, x, y ge 0`.

Answer

To solve the problem of maximizing \( Z = x + 2y \) subject to the constraints \( 2x + y \geq 3 \), \( x + 2y \geq 6 \), and \( x, y \geq 0 \), we will follow these steps:

### Step 1: Identify the Constraints
The constraints are:
1. \( 2x + y \geq 3 \)
2. \( x + 2y \geq 6 \)
3. \( x \geq 0 \)
4. \( y \geq 0 \)