If \( z=px+qy \), where \( p,q\gt 0 \), is the objective function, then the condition on \( p \) and \( q \) so that the maximum value of \( z \) occurs at A(4, 10) and B(6, 8), is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( p=q \)
If the maximum occurs at two corner points, z must have the same value at both of them.
\( z_A=4p+10q \)
\( z_B=6p+8q \)
\( 4p+10q=6p+8q \)
\( 2q=2p \)
\( p=q \)
Tip: When the optimum occurs at two corners, the objective line is parallel to the edge joining them, and every point on that edge gives the same optimal value.