For the linear programming problem(LPP),
Maximize $Z=4x+y$
$x + y ≤5$
$3x + y ≤9$
$x, y ≥0$.
Which of the following are NOT true?
(A) The given LPP has unbounded feasible region.
(B) The corner points of the feasible region are (0, 0), (0, 5), (3, 2) and (3, 0).
(C) The optimal value of the objective function is 12.
(D) The given LPP has a unique optimal solution.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A) and (B) only
Given LPP:
Maximize $Z=4x+y$
Subject to $x+y\le5,\;3x+y\le9,\;x\ge0,\;y\ge0$
Feasible region is bounded, so (A) is false.
So corner points are $(0,0),(0,5),(2,3),(3,0)$.
Given (B) lists $(3,2)$ instead of $(2,3)$, so (B) is false.
Compute $Z$ at corners:
$Z(0,0)=0$
$Z(0,5)=5$
$Z(2,3)=11$
$Z(3,0)=12$
Maximum value is $12$ at $(3,0)$, so (C) is true.
Only one point gives maximum, so (D) is true.
final answer: $\text{(A) and (B)}$