Question

The number of corner points of the feasible region determined by constraints \( x \geq 0, y \geq 0, x + y \geq 4 \) is:

• A. \( 0 \)
• B. \( 1 \)
• C. \( 2 \)
• D. \( 3 \)

Hint:

The number of corner points of a feasible region is determined by solving the intersection of the constraints.

Answer 1

The Correct Option is C

Step 1: Analyze the given constraints. \[ x \geq 0, \quad y \geq 0, \quad x + y \geq 4 \] These constraints represent: \begin{itemize} \( x \geq 0 \): Right of the y-axis. \( y \geq 0 \): Above the x-axis. \( x + y \geq 4 \): A line passing through points \( (4, 0) \) and \( (0, 4) \). \end{itemize} Step 2: Determine the feasible region. The feasible region lies in the first quadrant above the line \( x + y = 4 \). The intersection points (corner points) are: \[ (4,0), \quad (0,4) \] Final Answer: \[ \boxed{2} \]