The corner points of the bounded feasible region determined by the system of linear constraints are (0, 0), (5, 0), (6, 5), (6, 8), (4, 10), (0, 8). Let \(Z = 3x - 4y\) be the objective function. The minimum value of Z occurs at
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (0, 8)
On a bounded feasible region, the minimum of Z occurs at a corner point. The values of \(Z = 3x - 4y\) at the corners:
\(Z(0, 0) = 0\)
\(Z(5, 0) = 15\)
\(Z(6, 5) = 18 - 20 = -2\)
\(Z(6, 8) = 18 - 32 = -14\)
\(Z(4, 10) = 12 - 40 = -28\)
\(Z(0, 8) = 0 - 32 = -32\)
The smallest value is −32, at (0, 8).
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Linear Programming
