KCET · Maths · Linear Programming

Corner points of the feasible region for an LPP are \((0,2),(3,0),(6,0),(6,8)\) and \((0,5)\). Let \(Z=4 x+6 y\) be the objective function. The minimum value of \(z\) occurs at

A Only \((0,2)\)
B Only \((3,0)\)
C The mid-point of the line segment joining the points \((0,2)\) and \((3,0)\)
D Any point on the line segment joining the points \((0,2)\) and \((3,0)\)

Verified Solution

Answer & Solution

Correct Answer

(D) Any point on the line segment joining the points \((0,2)\) and \((3,0)\)

Step-by-step Solution

Detailed explanation

\(\therefore\) Minimum of \(Z\) occur at \((0,2)\) and \((3,0)\).
\(\therefore\) Minimum value of \(Z\) occur at any point on the line segment \((0,2)\) and \((3,0)\).

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Let \( S \) be the set of all real numbers. A relation \( R \) has been defined on \( S \) by \( a R b \Leftrightarrow |a-b| \leq 1 \),
then \( R \) is

KCET 2014 Medium

Match List-I with List-II

List-I		List-II
a)	A matrix which is not a square matrix	i)	Symmetric matrix
b)	A square matrix \(A = A'\)	ii)	Null matrix
c)	The diagonal elements of a diagonal matrix are same	iii)	Rectangular matrix
d)	A matrix which is both symmetric and skew symmetric	iv)	Scalar matrix

KCET 2026 Easy

Explore more questions on app

From KCET

Explore more questions on app