The point at which the minimum value of `z = 8x + 12y` subject to the constraints `2x +y ge 8, x + 2y ge 10 x ge 0, y ge 0` is obtained is

Options

A. (8,0)
B. (9, 1)
C. (2, 4)
D. (10, 0)

Answer

To find the point at which the minimum value of \( z = 8x + 12y \) is obtained subject to the constraints \( 2x + y \geq 8 \), \( x + 2y \geq 10 \), \( x \geq 0 \), and \( y \geq 0 \), we will follow these steps:

### Step 1: Identify the Constraints
The constraints given are:
1. \( 2x + y \geq 8 \)
2. \( x + 2y \geq 10 \)
3. \( x \geq 0 \)
4. \( y \geq 0 \)