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CBSE Class 12 Math 2022 Term I Solved Paper

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Question : 38 of 50
Marks: +1, -0
A Linear Programming Problem is as follows:
Maximise / Minimise objective function Z=2xyZ=2x-y +5+5
Subject to the constraints
3x+4y603x+4y \leq 60
x+3y30x+3y \leq 30
x0,y0x \geq 0, y \geq 0
If the corner points of the feasible region are A(0,10),B(12,6),C(20,0)A(0,10), B(12,6), C(20,0) and O(0,0)O(0,0), then which of the following is true?
Corner
Points
Value of Z=2xy+5Z=2x-y+5
A(0,10)A(0,10) Z=2(0)10+5=5Z=2(0)-10+5=-5 (Minimum)
B(12,6)B(12,6) Z=2(12)6+5=23Z=2(12)-6+5=23
C(20,0)C(20,0) Z=2(20)0+5=45Z=2(20)-0+5=45 (Maximum)
O(0,0)O(0,0) Z=0(0)0+5=5Z=0(0)-0+5=5
S the minimum value of Z is -5.
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