An objective function Z = ax + by is maximum at points (9, 3) and (5, 7) . If a, b ≥ 0 and ab = 16 , then the maximum value of the function is: - Mathematics MCQ Mathematics Mock Test - 11 2026 | ExamTest.live

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An objective function Z = a x + b y is maximum at points (9, 3) and (5, 7) . If a, b \geq 0 and ab = 16, then the maximum value of the function is:

Solution & Step-by-step Explanation

Since Z is maximum at both points, Z (9, 3) = Z (5, 7) : 9 a + 3 b = 5 a + 7 b ⟹ 4 a = 4 b ⟹ a = b Given ab = 16 : a \times a = 16 ⟹ a^{2} = 16 ⟹ a = 4 Since a = b, b = 4 .The maximum value Z = 4 (9) + 4 (3) = 36 + 12 = 48 .

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An objective function Z = a x + b y is maximum at points (9, 3) and (5, 7) . If a, b \geq 0 and ab = 16, then the maximum value of the function is:

48

78

108

148

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