# Word problems

• May 9th 2013, 07:36 PM
pczort
Word problems
I have three questions i cant seem to figure out, any help would be appreciated.

1) find two numbers whose sum is 84 such that the product of one number and the cube of the other number is a maximum

2) find two numbers whose sum is 78 such that the sum of their squares if a minimum

3)find two numbers who sum is 6 such that the sum of their cubes is a minimum.
• May 9th 2013, 07:42 PM
Gusbob
Re: Word problems
Quote:

Originally Posted by pczort
I have three questions i cant seem to figure out, any help would be appreciated.

1) find two numbers whose sum is 84 such that the product of one number and the cube of the other number is a maximum

2) find two numbers whose sum is 78 such that the sum of their squares if a minimum

3)find two numbers who sum is 6 such that the sum of their cubes is a minimum.

For 1), you have $x+y=84$ and $x^3y$ is maximum. You can think of $y$ as a function of $x$ via the equation $y=84-x$. Then the question reduces to finding the maximum of $x^3(84-x)$.

Similar constructions hold for 2) and 3). If you understood what I said the rest should be no problem.
• May 9th 2013, 07:47 PM
ibdutt
Re: Word problems
(1) take one number as x and the the second number would be ( 84 - x)
We want to maximize the product P = x^3 ( 84-x)
P' = 84*3 x^2 - 4x^3 = 252 x^2 - 4x^3
= 4x^2( 63 - x )

Now you can take it on
The other two are also similar and one can proceed on similar lines by forming equations.