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:

When determining corner points for feasible regions, find all intersections of the constraint boundaries and check where they satisfy the constraints.

Answer 1

The Correct Option is C

To determine the number of corner points of the feasible region, let us analyze the constraints: 1. \(x \geq 0\): 

This represents the region to the right of the \(y\)-axis, including the \(y\)-axis itself. 2. \(y \geq 0\): 

This represents the region above the \(x\)-axis, including the \(x\)-axis itself. 3. \(x + y \geq 4\): 

This represents the region above the line \(x + y = 4\). 

Rearranging, \(y = 4 - x\), which has intercepts at \(x = 4\) and \(y = 4\). 

The feasible region is the intersection of these constraints, which lies in the first quadrant (\(x \geq 0\), \(y \geq 0\)) and above the line \(x + y = 4\). The feasible region is unbounded but has two corner points: 

Intersection of \(x + y = 4\) with \(x = 0\): \((0, 4)\), - Intersection of \(x + y = 4\) with \(y = 0\): \((4, 0)\). Hence, the number of corner points is \(2\), and the correct answer is (C).