Max (z) = 5x + 10y subject to constraints:
\( x+2y\lt120 \)
\( x+y\gt60 \)
\( x-2y\gt0 \)
\( x,y\ge0 \)
Which of the following points do not lie in the feasible region of the above LPP ?
(A) (90, 15)
(B) (30, 15)
(C) (60, 20)
(D) (90, 10)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A) and (B) only
A point lies in the feasible region only if it satisfies every constraint. Here the constraints are strict (\( \lt \) and \( \gt \)), so a point on a boundary line is outside the region. Each point is checked against \( x+2y\lt120 \), \( x+y\gt60 \) and \( x-2y\gt0 \).
So (90, 15) fails \( x+2y\lt120 \) and (30, 15) fails \( x+y\gt60 \), while (60, 20) and (90, 10) satisfy all the constraints.
Each point below is marked by whether it lies in the feasible region; the answer is the points that do not, so they are the ones marked Incorrect.
Checking the statements
(A) (90, 15) — Incorrect. \( x+2y=90+30=120 \), which is not less than 120, so the point is not in the region.
(B) (30, 15) — Incorrect. \( x+y=45 \), which is not greater than 60, so the point is not in the region.
(C) (60, 20) — Correct. \( 100\lt120 \), \( 80\gt60 \) and \( 20\gt0 \), so the point is in the region.
(D) (90, 10) — Correct. \( 110\lt120 \), \( 100\gt60 \) and \( 70\gt0 \), so the point is in the region.