Question 1171437: Use linear programming.Find the value x and y that maximize and ,mininize the given objective function.
objective function:maximize and minimize P=5x+15y
subject to: x+3y=<=60
x+y=>=10
x-y<=0
x>=0
x>=0
please show the solution,thanks
Answer by greenestamps(13206)   (Show Source):
You can put this solution on YOUR website!
The constraints are....
(1) 
(2) 
(3) 
(4) 
(5)
Undoubtedly the last is supposed to be  ; however, with the other constraints, that one is unnecessary.
In this particular problem, finding the maximum value of the objective function is easy, using constraint (1):
So the maximum value of the objective function is going to be 300.
In the linear programming solution to the problem using a graph, this will correspond to the maximum value of the objective function being obtained anywhere along the portion of the graph of  that satisfies the other constraints.
The corners of the feasibility region are...
A(0,10) (intersection of (2) and (4)
B(0,20) (intersection of (1) and (4)
C(5,5) (intersection of (2) and (3)
D(15,15) (intersection of (1) and (3)
The objective function evaluated at those points is
A: 15(10) = 150
B: 15(20) = 300
C: 5(5)+15(5) = 25+75 = 100
D: 5(15)+15(15) = 75+225 = 300
Subject to the given constraints,
The minimum value of the objective function is 100, at (5,5).
The maximum value of the objective function is anywhere on the line x+3y=60 between (0,20) and (15,15).
|
|
|
