The corner points of the bounded feasible region for an L.P.P are (0, 10), (5, 5), (15,15), and (0, 20). If the objective function is \( Z=px+qy,p,q\gt 0 \), then the condition on \( p \) and \( q \) so that the maximum of \( Z \) occurs at (15, 15) and (0, 20) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 3p=q \)
If the maximum occurs at both points, Z has the same value at both:
\( 15p+15q=0\cdot p+20q \)
\( 15p=5q \)
\( 3p=q \)
With q = 3p, Z = 60p at both (15, 15) and (0, 20), which is more than Z = 20p at (5, 5) and Z = 30p at (0, 10). So this common value is indeed the maximum.
NCERT Exemplar:
Linear Programming
