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CBSE Class 12-science Answered

Find the maximum value of Z=7x+7y, subject to the constraints x?0 ,y?0,x+y?2 and 2x+3y?6 The answer given in the book is: Maximum Z=21 at x=3, y=0
Asked by Manoj | 18 Jun, 2013, 07:16: PM
answered-by-expert Expert Answer
If you will plot the 4 equations on a graph - x?0 ,y?0,x+y?2 and 2x+3y?6
 
and shade the region defined by the inequality, you will find that its a closed triangle, with vertices at A(0,2); B(2,0) and C(3,0)
 
Now to identify the point of maxima, we can find value of Z at each of these vertices. 
 
At point A: Z = 7(0) + 7(2) = 14
At point B: Z = 7(2) + 7(0) = 14
At point C: Z = 7(3) + 7(0) = 21
 
So, Z has a maximum value of 21 at point C (3,0)
Answered by | 19 Jun, 2013, 07:24: AM

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