CUET · MATHS · PYQ PAPER 2025
The corner points of the bounded feasible region determined by the system of linear constraints are \((0,8),(4,4)\), \((12,12),(0,20)\). Let \(z=p x+q y\), where \(p, q>0\). Condition on \(p\) and \(q\) so that the maximum of \(z\) occurs at both the points \((12,12)\), \((0,20)\) is
- A \(2 p=q\)
- B \(p =3 q\)
- C \(2 p =3 q\)
- D \(3 p =2 q\)
Answer & Solution
Correct Answer
(D) \(3 p =2 q\)
Step-by-step Solution
Detailed explanation
\(z(12,12) = p(12) + q(12) = 12p + 12q\) \(z(0,20) = p(0) + q(20) = 20q\) \(12p + 12q = 20q\) \(12p = 8q\) \(3p = 2q\)
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