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 pointCorrect
(D)does not exist

Answer: (C)

Solution

Maximise over the feasible region bounded by , , , . The objective cannot exceed 10 because of the constraint . Every point of the segment with (so ) is feasible: it satisfies and . At all

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Question ID VK-095080