If corner points of the bounded feasible region of a linear programming problem are as in the figure given below and \( z\ =\ px+qy,\ (p,q\gt 0) \) is an objective function. Then the relation between \( p \) and \( q \) , when \( z \) is maximum at D(4,10) and C(6,8), is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( p=q \)
If the maximum occurs at both D and C, z has the same value at the two points.
\( \displaystyle 4p+10q=6p+8q \)
\( \displaystyle 2q=2p \)
\( \displaystyle p=q \)