Let \( Z=ux+vy,\quad u,v\gt 0 \) be the objective function of a linear programming problem. Then the condition on \( u \) and \( v \) so that the maximum of \( Z \) occurs at both points (3, 4) and (0, 5) is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 3u=v \)
Z has its maximum at both (3, 4) and (0, 5) only if Z takes the same value at the two points:
\( \displaystyle Z(3,4)=3u+4v \)
\( \displaystyle Z(0,5)=5v \)
\( \displaystyle 3u+4v=5v \)
\( \displaystyle 3u=v \)
NCERT Exemplar:
Linear Programming
