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

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)