Question

PLEASE HELP!!!!
A company has found that the relationship between the price p and the demand x for a particular product is given approximately by
p=1269−0.2x2.
The company also knows that the cost of producing the product is given by C(x)=830+398x.

(A) Find P(x), the profit function.
P(x) =

Now use the profit function to do the following:

(B) Find the average of the x values of all local maxima of P.
Note: If there are no local maxima, enter "none".

Average of x values =

Answer 1

profit = revenue - cost

Answer 2

Profit = revenue - cost
we write this as function notation:
P(x) = R(x) - C(x)

P(x) = (number of units demanded x )* (price per unit when demand is x)- cost of making x units

P(X) = x*p - C(x)
P(X) = x * (1269 - .2x^2) - (830 + 398x)

Answer 3

Thank you, how exactly do you find part b?

Answer 4

first find the local maxima of P, then average them

Answer 5

this is P(x)

Answer 6

http://www.wolframalpha.com/input/?i=x+*+%281269+-+.2x^2%29+-+%28830+%2B+398x%29

Answer 7

these are the x values of the local maxima
http://prntscr.com/6xh8gx

Answer 8

the average is right in between , and due to symmetry, the average must be zero

Answer 9

It's saying zero is incorrect

Answer 10

is the first part correct

Answer 11

it wanted the exact amount at 38.1007, thank you very much

Answer 12

the average is 38.10007?

Answer 13

i believe it just wanted the local maxima

Answer 14

these are x values of the local maximum. and it is 38.1007, -38.1007
http://www.wolframalpha.com/input/?i=critical+points+x+*+%281269+-+.2x^2%29+-+%28830+%2B+398x%29

Answer 15

so that sounds right :)