CUET · MATHS · PYQ PAPER 2025
If the objective function \(Z=p x+q y, p>0, q>0\) of a linear programming problem attains its optimal value at the points \((4,7)\) and \((5,5)\) and \(pq =50\) then:
- A \(p=5, q=10\)
- B \(p=10, q=5\)
- C \(p=25, q=2\)
- D \(p=40 / 3, q=15 / 4\)
Answer & Solution
Correct Answer
(B) \(p=10, q=5\)
Step-by-step Solution
Detailed explanation
\(Z(4,7) = Z(5,5)\) \(p(4) + q(7) = p(5) + q(5)\) \(4p + 7q = 5p + 5q\) \(2q = p\) \(pq = 50 \implies (2q)q = 50\) \(2q^2 = 50 \implies q^2 = 25 \implies q = 5\) (\(q>0\)) \(p = 2(5) = 10\)
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