The maximum value of Z = x + y, subjected to x + y 10, 5x + 3y 15, x 6, x, y 0

MHT CET 2024 Mathematics question

Not in JEE syllabus

The maximum value of , subjected to , , ,

(A)occurs only at unique point
(B)occurs only at two distinct points
(C)occurs at infinitely many pointsCorrect
(D)does not exist

Answer: (C)

Solution

The objective is bounded above by the constraint , so . Points on the line that satisfy the other constraints give . On this line with (so ), and , so the constraint also holds. Thus every point of

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Question ID VK-092988