CUET · MATHS · PYQ PAPER 2023
For the objective function \(z=p x+q y\), where \(p, q>0\) the corner points of the feasible region determined by the system of linear constraints are \((0,10),(5,5),(15,15)\) and \((0,20)\), condition on \(p\) and \(q\) so that maximum of \(z\) occurs at both the points \((15,15)\) and \((0,20)\) is :
- A \(p=q\)
- B \(p=2 q\)
- C \(q=2 p\)
- D \(q=3 p\)
Answer & Solution
Correct Answer
(D) \(q=3 p\)
Step-by-step Solution
Detailed explanation
\(z(15,15) = p(15) + q(15) = 15p + 15q\) \(z(0,20) = p(0) + q(20) = 20q\) \(15p + 15q = 20q\) \(15p = 5q\) \(q = 3p\)
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