Solve the following linear programming problem graphically.
Minimize `:z=2x+3y-1`
Subject to:
`x-yge0`
`-x+2yge2`
`xge3`
`yle4`
`yge0`

Explanation

To solve the given linear programming problem graphically, we will follow these steps:

### Step 1: Identify the constraints
The constraints given in the problem are:
1. \( x - y \geq 0 \) (or \( x \geq y \))
2. \( -x + 2y \geq 2 \) (or \( 2y \geq x + 2 \) or \( y \geq \frac{1}{2}x + 1 \))
3. \( x \geq 3 \)
4. \( y \leq 4 \)
...