The bounded feasible region of an LPP is shown in the diagram given below.
The objective function \( z=3x+10y \) attains optimum values at:
A. Point (0,0)
B. Point (0,4)
C. Point (6,3)
D. Point (5,6)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → A and D only
The region is bounded, so by the corner point theorem both the maximum and the minimum of z occur at corner points. The corners are (0, 0), (4, 0), (6, 3), (5, 6) and (0, 4):
\( \displaystyle (0,0):\ z=0 \)
\( \displaystyle (4,0):\ z=12 \)
\( \displaystyle (6,3):\ z=18+30=48 \)
\( \displaystyle (5,6):\ z=15+60=75 \)
\( \displaystyle (0,4):\ z=40 \)
The optimum values are both the minimum and the maximum.
So the minimum value of z is 0 at (0, 0) and the maximum value is 75 at (5, 6).
Checking the statements
(A) Point (0,0) — Correct. The minimum z = 0 occurs here.
(B) Point (0,4) — Incorrect. z = 40 is neither the maximum nor the minimum.
(C) Point (6,3) — Incorrect. z = 48 is neither the maximum nor the minimum.
(D) Point (5,6) — Correct. The maximum z = 75 occurs here.