Question

Match List I with List II

	LIST I		LIST II
A.	The common region determined by all the linear constraints of a L.P.P. is called corner point	I.	corner point
B.	A point in the feasible region which is the intersection of two boundary lines is called,	II.	non-negative
C.	The feasible region for an LPP is always a	III.	feasible region
D.	The constraints \(x, y≥0\) describes that the variables involved in a LPP are	IV.	convex polygon

Choose the correct answer from the options given below:

• A. (A)-(I), (B)-(III), (C)-(IV), (D)-(II)
• B. (A)-(I), (B)-(III), (C)-(II), (D)-(IV)
• C. (A)-(IV), (B)-(II), (C)-(I), (D)-(III)
• D. (A)-(III), (B)-(I), (C)-(IV), (D)-(II)

Answer 1

The Correct Option is D

The problem involves matching concepts from linear programming problems (LPP) with their correct descriptions. Let's analyze each pair:

A.	The common region determined by all the linear constraints of a L.P.P. is called	I.	corner point
B.	A point in the feasible region which is the intersection of two boundary lines is called,	II.	non-negative
C.	The feasible region for an LPP is always a	III.	feasible region
D.	The constraints \(x, y≥0\) describes that the variables involved in a LPP are	IV.	convex polygon

Let’s map these descriptions correctly:

1. A - III: The common region determined by all the linear constraints of a LPP is the feasible region, which is where all constraints overlap and potential solutions exist.
2. B - I: A point in the feasible region that is the intersection of two boundary lines is a corner point. These points are crucial as they may contain the optimal solution.
3. C - IV: The feasible region for an LPP is always a convex polygon when linear inequalities are involved, since this ensures that for any two points within it, the line segment connecting them is also within the region.
4. D - II: The constraints \(x, y \geq 0\) ensure that the variables are non-negative, as all solutions must lie in the first quadrant.

The correct matching is:

(A)-(III), (B)-(I), (C)-(IV), (D)-(II)