SOLUTION: graph each system of constraints. find all vertices. evaluate the objective function at each vertex to find teh maximum or minimum value..:) *** all the < and > have lines under

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Question 176608: graph each system of constraints. find all vertices. evaluate the objective function at each vertex to find teh maximum or minimum value..:)
*** all the < and > have lines under neath them.. so all the arrows are equal or greater than...


1)x<3
y<7
x>0,y>0
maximum for p=2x+3y



2) 2x+y<30
x+y<20
x>0, y>0
minimum for c=x+4y



Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1)0+%3C=++x+%3C=+3
0+%3C=+y+%3C=+7

P%28x%2Cy%29=2x%2B3y
P%280%2C0%29=2%280%29%2B3%280%29=0
P%283%2C0%29=2%283%29%2B3%280%29=6
P%283%2C7%29=2%283%29%2B3%287%29=27
P%280%2C7%29=2%280%29%2B3%287%29=21
Max. value=27 occuring at (3,7), min. value =0 occuring at (0,0).
.
.
.
2)First find the feasible region bounded by the lines,
2x%2By%3C=30
y%3C=30-2x
.
.
.
x%2By%3C=20
y%3C=20-x
.
.
.
x%3E=0
y%3E=0
Let's look at the graph of the two lines.
The vertices are then the x-intercept and y-intercept of the graphs.
+graph%28+300%2C+300%2C+-2%2C+18%2C+-2%2C+38%2C+20-x%2C+30-2x%29+
Y-intercept: (0,20)
X-intercept: (15,0)
The final point is their intersection point.
30-2x=20-x
x=10
y=10

C%28x%2Cy%29=x%2B4y
C%280%2C0%29=0%2B4%280%29=0
C%2815%2C0%29=15%2B4%280%29=15
C%2810%2C10%29=10%2B4%2810%29=50
C%280%2C20%29=0%2B4%2820%29=80
The minimum for C=x+4y is 0 and occurs at (0,0).