Maximize Z=4x+9y, subject to constraints x?0,y?0,x+5y?200,2x+3y?134 The answer given in the book is: Maximum Z=382 when x=10 and y=38

if you draw a graph for the given 4 constraint equation --  x?0,y?0,x+5y?200,2x+3y?134 and identify the polygon enclosed by the equations, you will find that its is a quadrilateral, with A(0,0); B(67,0); C(10,38); D(0,40)

 

Now since its an enclosed area, the maximum value of Z should be at one of the vertices. 

 

hence, at A(0,0); Z = 4(0) + 9(0) = 0

at B(67,0); Z = 4(67) + 9(0) = 268

at C(10,38); Z = 4(10) + 9(38) = 382

at D(0,40); Z = 4(0) + 9(40) = 360

 

So, the maximum value of Z is at C(10,38) and the value is 382.