The corner points of the bounded feasible region determined by \( 2x+y\le 10\ ,\ x+3y\le 15,\ x,y\ge 0 \) are (0, 0), (5, 0) , (3, 4) and (0, 5). Let \( z=px+qy,\ p,q\gt 0 \), then the relation between \( p \) and \( q \) so that the maximum of \( z \) occurs at both (3, 4) and (0, 5 ), is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( q=3p \)
If the maximum occurs at both points, z has the same value at both.
\( \displaystyle 3p+4q=0\cdot p+5q \)
\( \displaystyle 3p=q \)