The corner points of the feasible region for an LPP are (0, 10), (5, 5), (15, 15) and (0, 20). If the objective function is \(Z=px+qy\), \(q \gt 0\), then the condition so that the maximum of Z occurs at (15, 15) and (0, 20) is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(q=3p\)
For the maximum to occur at both (15, 15) and (0, 20), Z must take the same value at these two corners:
\(15p + 15q = 0p + 20q\)
\(15p = 5q\)
\(q = 3p\)
Check that this common value is the maximum. With q = 3p (so p > 0):
\(Z(0, 10) = 30p,\quad Z(5, 5) = 20p\)
\(Z(15, 15) = 60p,\quad Z(0, 20) = 60p\)
The largest value 60p is reached at (15, 15) and (0, 20), as required.
NCERT Exemplar:
Linear Programming
