Quadratic Functions

[shanieO]

Need some help with this question please:
A firm can sell X units at a price of P cents per unit, where P=503-x. The total costs of production is given by the function T(X) = 500 + 2X.
a) Find the function that relates total revenue to the number of units sold - R(X)
I have R(X) = (503-x)x R(X) = 503x-x^2
b) Find the function that relates total profit to the number of units sold -P(X)
I have P(X) = R(X) - C(X) P(X) = (503x-x^2) - (500+2x)
P(X) = 501x - x^2 - 500
c) Find the number of units to be sold to achieve maximum profit and find the maximum profit.
Now I am lost.
d) What price per unit would the firm be charging at the maximum profit output level?
Lost with this one also.

Would appreciate any help I could get.

Need answer before March 12, 2006 :? :?

 

[robbwrr]

\(\displaystyle f(x)=ax^2 + bx +c = a(x+\frac{b}{2a})^2 + (c - \frac{b^2}{4a})\) after completing the square.

This is how to transform any quadratic to y=a(x-h)^2 + k form.

If a < 0 then it will have a maximum of y=k at x=h
(minimum if a>0)

Apply this to your formula in b) to answer the last two questions.