# SOLUTION: Hello. I'm having problems with maximums in linear programming. What is the maximum value of z=3x+y for the region given by the system: x>= 0 y>= 0 1/2x+y<=11 3x+2y<= 30 I

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 Click here to see ALL problems on Linear Equations And Systems Word Problems Question 91307: Hello. I'm having problems with maximums in linear programming. What is the maximum value of z=3x+y for the region given by the system: x>= 0 y>= 0 1/2x+y<=11 3x+2y<= 30 I'm sure you have to plot a graph and find the feasible region. I just can't remember how to plot the graph correctly. Thanks so much.Answer by stanbon(57378)   (Show Source): You can put this solution on YOUR website!What is the maximum value of z=3x+y for the region given by the system: x>= 0 y>= 0 These two conditions limit the search to the 1st Quadrant. ------------------------------------- 1/2x+y<=11 Solve for y so you can graph this restriction: y <= (-1/2)x + 11 --------------- Find the coordinates of the intersection points of the restricion lines. Put those coordinate vales into the objective function, z=3x+y, and see which coordinate pair give a maximum value. ======================= Cheers, Stan H.