[portillo]

Hi, I have problem with this question. Hope you can find a solution for this question.

Philip, the proprietor of a vineyard, estimates at the first 10000 bottles of wine produce this season will fetch a profit of $5 per bottle. However, the profit from each bottle beyond 10000 drop by $0.0002 for each additional bottle sold. Assuming at least 10000 bottles of wine are produced and sold, what is the maximum profit? What would be the price per bottle in this case?

[kristo]

Let's make a quadratic function of this, x being the number of bottles sold. Money he gets from selling wine is price per bottle*bottles sold.
f(x)=5*10000 + x(5-0,0002x)
f(x)=-0,0002x^2 + 5x + 50000
-0,0002x^2 + 5x + 50000 is a quadratic function of a form ax^2 + bx + c and every quadratic of this form can be written as a(x-h)^2+k
k is the maximum value and h is the number of bottles sold for maximum value.
The formula for finding them is:
h=-b:2a
k=f(-b:2a)

[portillo]

I'm sorry... I'm still not sure how to find the ans

[Capuchin]

You know how to solve a quadratic don't you? I would assume that this is the point of the problem.