Question

FInd 2 posetive numbers such that their product is 185 and their sum is a minimum. (optimization)

Answer 1

using calculus ?

Answer 2

Yes :)

Answer 3

let the 2 numbers be x and y
so , xy= ?
function to be minimised = x+y= ?

Answer 4

xy=185
i dont understand the 2nd part

Answer 5

xy =185
so find y from this(or x)
then put it in f=x+y

Answer 6

oh. so do i put f in for y in xy=185?

Answer 7

y=185/x
f(x) = x + 185/x
got this ?
now miminize f(x)
know how to ?

Answer 8

ohhhh! ok. let me process this x)

Answer 9

sure, take your time :)

Answer 10

Take the derivative?

Answer 11

yes!
take derivative and equate it to ..... ?

Answer 12

0 ~(^_^)~

Answer 13

absolutely!

Answer 14

so what derivative u got ?
f'(x) = ?

Answer 15

1+ (185/x^2)

Answer 16

then do I solve for x?

Answer 17

sure? no sign mistakes ?

Answer 18

Oops! Its "-" not "+" x)

Answer 19

right.
and yes now equate that to 0

Answer 20

1- (185/x^2) =0
x= ?

Answer 21

\[\sqrt{185}\]

Answer 22

yes!
actually u also get -sqrt(185) but since the numbers are positive, u only get x=+sqrt(185)
got this ?

Answer 23

oh, yeah. Got it.

Answer 24

Now do I take the second derivitive?

Answer 25

i don't think that required, u got x, now find y and u are done.....

Answer 26

So.. find y by putting the answere I got for x into the xy=185?

Answer 27

yup.

Answer 28

the answere is \[\sqrt{185}\] for both! :D

Answer 29

yes!

Answer 30

Thank u sooo much!

Answer 31

welcome sooo much!