Posted by **Aria** on Wednesday, July 20, 2011 at 7:26pm.

If the profit equation for the monthly sales of tile sets is P = -x^2 + 56x - 300, how do I find the number of tiles that yeilds the most profit.

x=number of tile sets. The amount of money for costs each month is set at $300.

I saw an answer as 28 tile sets would yeild the highest profit but I don't understand why that is the answer, if it is.

Could you help me? Thanks so much.

- Algebra -
**Damon**, Wednesday, July 20, 2011 at 8:24pm
x^2 -56 x = -p - 300

complete the square to find vertex of parabola

x^2 -56 x + 784 = -p +484

(x-28)^2 = - (p-484)

so

vertex (max of p) is at (28,484)

- Algebra -
**Aria**, Wednesday, July 20, 2011 at 9:12pm
Damon,

Why does this explain the highest yeild?

It sounds like what you did was on a graph and you found the highest points

- Algebra -
**Linda**, Monday, November 14, 2011 at 2:25pm
-4x^3 + 24x^2 – 24x + 4 by x^2 – 5x + 1

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