Question

PLEASE HELP!
A company plans to sell bicycle helmets for $26 each. The company's business manager estimates that the cost, y, of making x helmets is a quadratic function with a y-intercept of 8,400 and a vertex of (500, 15,900).
y = 26x and y = -0.030(x-500)2+15,900

How many helmets must the company make and sell to break even?
____ helmets

Ive been trying to figure it out but I keep making a mistake and I don't know where I am messing up on the problem

Answer 1

\(\rm y = 26x\) is the `sale price` for selling x helmets.

\(\rm y = -0.030(x-500)2+15,900\) is the `cost` to make x helmets.

So the profit made on x helmets is the `sale price` minus the `cost` to make them.

\[\large\rm profit=26x-(-0.030(x-500)^2+15,900)\]

Answer 2

So ummm

Answer 3

We want to know when a profit of zero is made, no profit, break even.\[\large\rm 0=26x-(-0.030(x-500)^2+15,900)\]Ya I think that's what they want... I think.

Answer 4

And you would have to solve for x from this point.

Answer 5

Thank you!!!