Question

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

• A. 0
• B. 1
• C. 2
• D. 3
• E.

Hint:

For linear programming problems, the corner points of the feasible region are determined by the intersection of the constraints. Always consider the boundary conditions of the inequalities.

Answer 1

The Correct Option is C

The constraints are: \[ x \geq 0, \quad y \geq 0, \quad x + y \geq 4. \] 1. Constraint Interpretation: * \( x \geq 0 \): Region is to the right of the \( y \)-axis. * \( y \geq 0 \): Region is above the \( x \)-axis. * \( x + y \geq 4 \): Region is on or above the line \( x + y = 4 \). 2. Feasible Region: This region is the intersection of the constraints within the first quadrant. The line \( x + y = 4 \) intersects the axes at \( (4, 0) \) and \( (0, 4) \). As \( x \geq 0 \) and \( y \geq 0 \), these points define the boundary. The feasible region is unbounded, with corner points at \( (4, 0) \) and \( (0, 4) \). 3. Corner Point Count: There are exactly two corner points in the feasible region. Therefore, the answer is (C) 2.