The corner points of the bounded feasible region of a linear programming problem are \((2, 1)\), \((6, 1)\), \((5, 4)\) and \((1, 3)\). If \(Z = 3x + 2y\) is the objective function, then (maximum value of Z) − (minimum value of Z) is equal to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 15
The region is bounded, so both the maximum and the minimum of Z occur at corner points. Values of \(Z = 3x + 2y\):
\(Z(2, 1) = 6 + 2 = 8\)
\(Z(6, 1) = 18 + 2 = 20\)
\(Z(5, 4) = 15 + 8 = 23\)
\(Z(1, 3) = 3 + 6 = 9\)
The maximum is 23 and the minimum is 8.
\(23 - 8 = 15\)