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.

Question

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.

Answer 1

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)

Answer 2

Damon,
Why does this explain the highest yeild?

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

Answer 3

-4x^3 + 24x^2 – 24x + 4 by x^2 – 5x + 1