Corner points of the bounded feasible region determined by the system of linear constraints are (0, 3), (1, 1), and (3, 0). Let \( Z=px+qy \) , where \( p,q\gt 0 \). Condition on \( p \) and \( q \) so that the minimum of Z occurs at (3, 0) and (1, 1) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 2p=q \)
If the minimum occurs at two corner points, Z must have the same value at both.
\( \displaystyle Z(3,0)=3p \)
\( \displaystyle Z(1,1)=p+q \)
\( \displaystyle 3p=p+q \)
\( \displaystyle 2p=q \)
With q = 2p, Z(0, 3) = 3q = 6p, which is larger than 3p, so the minimum is indeed at (3, 0) and (1, 1).
NCERT Exemplar:
Linear Programming
