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Science-Related Homework Help Mathematics Topic started by: Smith11 on Apr 3, 2013



Title: Find two positive numbers that minimize the sum of twice the first number plus second if product of two is 288?
Post by: Smith11 on Apr 3, 2013
This is calculus optimization problem. In a book answers are 12 and 24.
Please show how you did it.
Thank you.


Title: Find two positive numbers that minimize the sum of twice the first number plus second if product of two is 288?
Post by: smartgirl777 on Apr 3, 2013
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Title: Find two positive numbers that minimize the sum of twice the first number plus second if product of two is 288?
Post by: Juelz_9214 on Apr 3, 2013
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