If the objective function \( z=10(x-7y+190) \) and the corner points of the bounded feasible region are A(0,4), B(0,5), C(3,5), D(5,3), E(5,0), F(4,0), then the minimum value of z will be:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1550
On a bounded feasible region the minimum occurs at a corner point. The values of z = 10(x − 7y + 190) at the corners are:
\( A(0,4):\ z=10(0-28+190)=1620 \)
\( B(0,5):\ z=10(0-35+190)=1550 \)
\( C(3,5):\ z=10(3-35+190)=1580 \)
\( D(5,3):\ z=10(5-21+190)=1740 \)
\( E(5,0):\ z=10(5+190)=1950 \)
\( F(4,0):\ z=10(4+190)=1940 \)
The minimum value is 1550, at B(0, 5).