Question 73140This question is from textbook
: find the maximum and minimum values of
T= 6x + 10y subject to
x+y < or = to 10
5x + 10y > or = 50
x > or = 2
y > or = 0
Can you possibly help me with this?
Thank You
This question is from textbook
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! find the maximum and minimum values of
T= 6x + 10y subject to
x+y < or = to 10
5x + 10y > or = 50
x > or = 2
y > or = 0
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T = 6x+10y is the object function to be evaluated.
Solve the next two for y:
y<=-x+10
y>=(-1/2)x+5
x>=2 defines the domain for the object function
y>=0 defind the range for the object function
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Draw a coordinate system.
Draw a vertical line at x=2
Shade the area to the right of x=2 where y>0
Graph the line y=(-1/2)x+5 (shade the area above the line)
Graph the line y=-x+10 (shade the area below the line)
Find the coordinates of the points of intersection of the three lines: x=2;
y=-x+10; y=(-1/2)x+5
They are (2,4), (2,8), and (10,0)
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Evaluate T=6x+10y for these three points:
If (2,4), then T=6*2+10*4 = 52 (minimum point)
If (2,8), then T=6*2+10*8 = 92 (maximum point)
If (10,0), thenT=6*10+10*0 = 60
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Cheers,
Stan H.
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