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

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> 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      Log On


   

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(75887) About Me  (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
graph%28400%2C300%2C-10%2C25%2C-10%2C25%2C%28-1%2F2%29x+%2B+11%29
---------------
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.
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Cheers,
Stan H.