# Maximization Problem

• May 21st 2011, 11:55 AM
jennifer92
Maximization Problem
I am trying to find what value X needs to be to make the maximum value for Y, but I am not sure how to do that!

Code:

```X  |  Y --------- 0.6 | 1112 0.7 | 1113.5 0.8 | 1107```
• May 21st 2011, 12:14 PM
TKHunny
x = 0.7?

If this is not the correct answer, you'll have to provide a better problem statement.
• May 21st 2011, 12:27 PM
jennifer92
Code:

`( 80(1-x) + 107 )( 5x + 5 ) = y`
That is the equation I drew up. I need to know what X needs to be so that Y is as high of a number as possible.

If X = 0.66 then Y = 1113.86
If X = 0.67 then Y = 1113.89
If X = 0.68 then Y = 1113.84

So I know the answer is somewhere between 0.66 and 0.67
• May 21st 2011, 02:57 PM
topsquark
Quote:

Originally Posted by jennifer92
Code:

`( 80(1-x) + 107 )( 5x + 5 ) = y`
That is the equation I drew up. I need to know what X needs to be so that Y is as high of a number as possible.

If X = 0.66 then Y = 1113.86
If X = 0.67 then Y = 1113.89
If X = 0.68 then Y = 1113.84

So I know the answer is somewhere between 0.66 and 0.67

Are you required to use a numerical solution here? Your function y(x) is a quadratic and there is a process you can use for this...completing the square. Can you use this method?

-Dan
• May 21st 2011, 04:54 PM
jennifer92
I can solve the problem using any method!
• May 21st 2011, 05:40 PM
topsquark
Quote:

Originally Posted by jennifer92
I can solve the problem using any method!

Okay, so let me ask you the following... Your problem boils down to finding the maximum of $y = -400x^2 + 535x + 935$. This is a parabola that opens downward, so it has a maximum. The maximum will lie on the axis of symmetry of the parabola and is, in fact, at the vertex. Can you find the vertex of this parabola?

-Dan
• May 21st 2011, 05:48 PM
jennifer92
Quote:

Originally Posted by topsquark
Okay, so let me ask you the following... Your problem boils down to finding the maximum of $y = -400x^2 + 535x + 935$. This is a parabola that opens downward, so it has a maximum. The maximum will lie on the axis of symmetry of the parabola and is, in fact, at the vertex. Can you find the vertex of this parabola?

-Dan

How did you convert it to $y = -400x^2 + 535x + 935$ ?

And I am not sure what a vertex is. The only information I have is the original formula I gave you.
• May 21st 2011, 06:13 PM
topsquark
Quote:

Originally Posted by jennifer92
How did you convert it to $y = -400x^2 + 535x + 935$ ?

And I am not sure what a vertex is. The only information I have is the original formula I gave you.

I multiplied your expression out and simplified it. A vertex is a maximum point (up, down, left, or right) on a parabola. This is a Pre-Calculus level question, yes?

-Dan
• May 21st 2011, 06:36 PM
jennifer92
Thanks for your help, I got it figured out.