CUET · MATHS · PYQ PAPER 2025
The corner points of the bounded feasible region for a linear programming problem (LPP) are \(\left(0, \frac{3}{2}\right),(1,2)\) and \((4,0)\).
If the objective function is \(Z=a x+b y\), where \(a\) and \(b\) are positive,
then the condition on \(a\) and \(b\) so that the maximum of \(Z\) occurs at \((1,2)\) and \((4,0)\) is :
- A \(a=2 b\)
- B \(2 a=b\)
- C \(3 a=2 b\)
- D \(3 a=4 b\)
Answer & Solution
Correct Answer
(C) \(3 a=2 b\)
Step-by-step Solution
Detailed explanation
\(Z(1,2) = a(1) + b(2) = a+2b\) \(Z(4,0) = a(4) + b(0) = 4a\) \(Z(1,2) = Z(4,0) \implies a+2b = 4a\) \(2b = 3a\)
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