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Home Q & A Board Science-Related Homework Help Mathematics
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Smith11 Smith11
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9 years ago
This is calculus optimization problem. In a book answers are 12 and 24.
Please show how you did it.
Thank you.
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smartgirl777smartgirl777
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9 years ago
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I already answered this on you other post,
but here it is again

call the two number x and y
xy=288
x=288/y

2x+y=min
2(288/y)+y=min
576/y+y=min
take the derivative
-576/y^2+1=0
-576/y^2=-1
576=y^2
y=24

xy=288
24x=288
x=12
1

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wrote...
#2
9 years ago
Let x and y be the two numbers so that S=2x+y and xy=288.

Solve the second equation for one of the variables
x=288/y.

Plug this in to the first equation.
S=576/y+y

Take the derivative.

dS/dy=-576/y^2+1

Set dS/dy = 0 and solve for y.

y^2-576=0
y=24

24x=288
x=12
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