Question 45411: Can you show me the steps to solve this problem?
Find the maximum value of p=5x+2y under the following conditions.
x>0 y>0 2x+y<10 x+y<7
All symbols are greater than or equal to, or less than and equal to.
Thanks in advance.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find the maximum value of p=5x+2y under the following conditions.
x>0 y>0 2x+y<10 x+y<7
Draw an x,y coordinate system.
x>0 and y>0 mean we are looking at the 1st quadrant.
Graph y<-2x+10
Graph y< -x+7
Find the coordinates of the four intersection points, as follows:
Find the intersection of the two lines, y=-2x+10 and y=-x+7; it is (3,4)
Find the intersection of y=-2x+10 and y=0; it is (5,0)
Find the intersection of y=-x+7 and x=0; it is (0,7)
Find the intersection of x=0 and y=0; it is (0,0)
Hopefully you can see these intersection points.
Now, evaluate p=5x+2y with the values of these intersection points, as follows:
(0,0); p=5(0)+2(0)=0
(0,7): p=5(0)+2(7)=14
(5,0): p=5(5)+2(0)=25
(3,4): p=5(3)2(4)=23
From this you can see that the maximum value of p is p=25 and
that occurs when x=5 and y=0
Cheers,
Stan H.
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