The corner points of the bounded feasible region of a linear programming problem are \((2, 0)\), \((5, 0)\), \((6, 3)\), \((1, 6)\) and \((0, 4)\). The minimum value of the objective function \(Z = x - 3y\) is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(-17\)
On a bounded region, the minimum of Z occurs at a corner point. Values of \(Z = x - 3y\):
\(Z(2, 0) = 2\)
\(Z(5, 0) = 5\)
\(Z(6, 3) = 6 - 9 = -3\)
\(Z(1, 6) = 1 - 18 = -17\)
\(Z(0, 4) = -12\)
The smallest value is \(-17\), at (1, 6).