# Thread: Maximization Problem

1. ## 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

2. x = 0.7?

If this is not the correct answer, you'll have to provide a better problem statement.

3. 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

4. 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

5. I can solve the problem using any method!

6. 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 $\displaystyle y = -400x^2 + 535x + 935$. 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

7. Originally Posted by topsquark
Okay, so let me ask you the following... Your problem boils down to finding the maximum of $\displaystyle y = -400x^2 + 535x + 935$. 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 $\displaystyle y = -400x^2 + 535x + 935$ ?

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

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

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

9. Thanks for your help, I got it figured out.