If the objective function for an LPP is \(z=3x-4y\) and corner points for bounded feasible region are (5, 0), (6, 5) and (4, 10), then :
(A) maximum value of \(z\) is 2
(B) minimum value of \(z\) is 2
(C) maximum value of \(z\) is at (5, 0)
(D) no maximum value of \(z\)
(E) maximum value of \(z\) is 15
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (C) and (E) Only
For a bounded feasible region, z has both a maximum and a minimum, and they occur at corner points. Values of z = 3x − 4y:
\(z(5, 0) = 15\)
\(z(6, 5) = 18 - 20 = -2\)
\(z(4, 10) = 12 - 40 = -28\)
So the maximum of z is 15, at (5, 0), and the minimum of z is −28, at (4, 10).
Checking the statements
(A) maximum value of \(z\) is 2 — Incorrect. The maximum is 15.
(B) minimum value of \(z\) is 2 — Incorrect. The minimum is −28.
(C) maximum value of \(z\) is at (5, 0) — Correct. z = 15 there, the largest corner value.
(D) no maximum value of \(z\) — Incorrect. The region is bounded, so z has a maximum (15).
(E) maximum value of \(z\) is 15 — Correct. z(5, 0) = 15 is the largest corner value.