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Find two positive numbers that minimize the sum of twice the first number plus second if product of two is 288?
Smith11
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Find two positive numbers that minimize the sum of twice the first number plus second if product of two is 288?
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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smartgirl777
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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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Juelz_9214
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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