Maximise `Z= 3x + 2y` subject to `x + 2y le 10, 3x + y le 15, x, y ge 0`.

Answer

To solve the problem of maximizing \( Z = 3x + 2y \) subject to the constraints \( x + 2y \leq 10 \), \( 3x + y \leq 15 \), and \( x, y \geq 0 \), we can follow these steps:

### Step 1: Identify the Constraints
The constraints are:
1. \( x + 2y \leq 10 \) (Constraint 1)
2. \( 3x + y \leq 15 \) (Constraint 2)
3. \( x \geq 0 \) (Non-negativity constraint)
4. \( y \geq 0 \) (Non-negativity constraint)