The corner points of the feasible region of a LPP are (0,2), (3, 0), (6, 0), (6, 8) and (0, 5). If the objective function is \( z=4x+6y \), then the sum of maximum and minimum value of z is equal to:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 84
The values of z = 4x + 6y at the corner points are:
\( \displaystyle z(0,2)=12 \)
\( \displaystyle z(3,0)=12 \)
\( \displaystyle z(6,0)=24 \)
\( \displaystyle z(6,8)=24+48=72 \)
\( \displaystyle z(0,5)=30 \)
Maximum = 72 at (6, 8); minimum = 12, at both (0, 2) and (3, 0) (and at every point of the edge joining them).
\( \displaystyle \text{Sum}=72+12=84 \)
Why the other options are incorrect
Option (1) 72 — Incorrect. 72 is the maximum value alone.
Option (3) 96 — Incorrect. 96 = 72 + 24 takes the minimum as 24, the value at (6, 0); the smallest corner value is 12.
Option (4) 102 — Incorrect. 102 = 72 + 30 adds the value at (0, 5), which is not the minimum.