If the objective function for an LPP is \( Z=2x+5y \) and the corner points of the bounded feasible region are (0, 0), (5, 0), \( \left(\displaystyle\frac{8}{5},\frac{6}{5}\right) \) and (0, 2) then the maximum value of z occurs at
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → all points joining the line segment with points (5,0) and (0,2)
Values of Z = 2x + 5y at the corner points:
(0, 0): 0
(5, 0): 10
\( \left(\frac85,\frac65\right) \): \( \frac{16}{5}+6 = 9.2 \)
(0, 2): 10
The maximum value 10 occurs at two corner points, (5, 0) and (0, 2). When the maximum occurs at two corner points, it occurs at every point of the line segment joining them.
Why the other options are incorrect
Option (1) (5,0) — Incorrect. Z is 10 at (5, 0), but (0, 2) gives the same value, so (5, 0) is not the only point of maximum.
Option (2) \( \left(\frac{8}{5},\frac{6}{5}\right) \) — Incorrect. Z = 9.2 there, less than 10.
Option (3) (2, 0) — Incorrect. It is not a corner point, and Z = 4 there.