If the optimal value of the objective function \(z = px + y\) of an L.P.P occurs at two corner points (2, 11) and (4, 5) of its bounded feasible region, then its optimal value is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 17
Since the optimal value occurs at both corner points, z has the same value at both:
\(z(2, 11) = 2p + 11\)
\(z(4, 5) = 4p + 5\)
\(2p + 11 = 4p + 5\)
\(2p = 6,\quad p = 3\)
So \(z = 3x + y\), and the optimal value is:
\(z(2, 11) = 3(2) + 11 = 17\)
As a check, \(z(4, 5) = 3(4) + 5 = 17\).