The maximum value of the objective function \(Z = px + 2y\) on a bounded feasible region occurs at the two corner points \((1, 8)\) and \((5, 2)\). The maximum value of Z is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 19
Since the maximum occurs at both points, Z has equal values there:
\(p(1) + 2(8) = p(5) + 2(2)\)
\(p + 16 = 5p + 4\)
\(4p = 12\)
\(p = 3\)
So \(Z = 3x + 2y\), and the maximum value is
\(Z(1, 8) = 3 + 16 = 19\)
Check: \(Z(5, 2) = 15 + 4 = 19\).