The minimum value of `Z = 4x + 5y` subjected to the constraints `x + y ge 6, 5x + y ge 10 , x ge 0, y ge 0` is

Options

A. 28
B. 24
C. 30
D. 31

Answer

To find the minimum value of \( Z = 4x + 5y \) subject to the constraints \( x + y \geq 6 \), \( 5x + y \geq 10 \), \( x \geq 0 \), and \( y \geq 0 \), we will follow these steps:

### Step 1: Identify the constraints
The constraints are:
1. \( x + y \geq 6 \)
2. \( 5x + y \geq 10 \)
3. \( x \geq 0 \)
4. \( y \geq 0 \)