The corner points O, A, B, C, D and E of the bounded feasible region determined by the system of linear constraints are shown in the given figure.
If \( z=3x-4y \) be the objective function, then the minimum of \( z \), is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( -32 \)
The feasible region is bounded, so the minimum of z occurs at a corner point. From the figure the corners are O(0, 0), A(0, 8), B(4, 10), C(6, 8), D(6, 5) and E(4, 0).
Value of \( z=3x-4y \) at each corner:
\( \displaystyle O(0,0):\ z=0 \)
\( \displaystyle A(0,8):\ z=0-32=-32 \)
\( \displaystyle B(4,10):\ z=12-40=-28 \)
\( \displaystyle C(6,8):\ z=18-32=-14 \)
\( \displaystyle D(6,5):\ z=18-20=-2 \)
\( \displaystyle E(4,0):\ z=12-0=12 \)
The smallest value is −32, at A(0, 8).
NCERT Exemplar:
Linear Programming
