The maximum and minimum values of the objective function Z = x + 2y subject to the constraints
` x+2y ge 100, 2x -y le 0, 2x +y le 200` occurs respectively at

Options

A. one point and three points
B. two points and one point
C. one point and infinitely points
D. one point and one point

Explanation

To solve the problem of finding the maximum and minimum values of the objective function \( Z = x + 2y \) subject to the constraints \( x + 2y \geq 100 \), \( 2x - y \leq 0 \), and \( 2x + y \leq 200 \), we will follow these steps:

### Step 1: Write down the constraints
The constraints given are:
1. \( x + 2y \geq 100 \)
2. \( 2x - y \leq 0 \) (which can be rewritten as \( y \geq 2x \))
3. \( 2x + y \leq 200 \)