SOLUTION: find the maximum value of the objective function z=3x+5y subject to the folloing constraints: x greater than or equal to 2, y greater than or equal to 0, x+y less than or equal to

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: find the maximum value of the objective function z=3x+5y subject to the folloing constraints: x greater than or equal to 2, y greater than or equal to 0, x+y less than or equal to       Log On


   

Question 251014: find the maximum value of the objective function z=3x+5y subject to the folloing constraints: x greater than or equal to 2, y greater than or equal to 0, x+y less than or equal to 6.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Graph the constraints to find the feasible region.
x%3E=2
y%3E=0
x%2By%3C=6
y%3C=6-x

As we see the feasible region is a triangle with vertices at (2,0),(2,4),and (0,6).
The max and min of the objective function occurs at one of these vertices.
(2,0): +z=3x%2B5y=3%282%29%2B5%280%29=6
(2,4): +z=3x%2B5y=3%282%29%2B5%284%29=26
(6,0): +z=3x%2B5y=3%286%29%2B5%280%29=18
The max value of 26 occurs at (2,4).