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Maximum value of Z = 12x + 3y subject t...

Maximum value of Z = 12x + 3y subject to constraints ` x ge 0,y ge 0, x+y le 5 ` and ` 3x+y le 9` is

A

15

B

36

C

60

D

40

Text Solution

Verified by Experts

The correct Answer is:
B
Given constraints are ` x ge 0, y ge 0, x+y le 5 ` and ` 3x+ y le 9.`
Objective fucntion max Z= 12x +3y
Here, feasible region is OABCO.
` (##ARH_EGN_PRG_MAT_C17_E01_038_S01.png" width="80%">
At point O (0, 0), Z = 12 (0) + 3(0) = 0
At point A (3, 0), Z = 12(3) + 3(0) = 36
At point B (2, 3), Z = 12(2) + 3(3) = 33
At point C (0, 5), Z = 12(0) + 3(5) = 15
Hence, maximum "'.alue of Z is 36
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