# 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 =

1 answer

###### Question:

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 =

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 =

## Answers

We know that the profit from an item is the sale price minus the cost price. Thus,1269 - 0.2x² - 830 - 398xP(x) = -0.2x² - 398x + 439Local maxima are located at the points where the first derivative of a function are 0P'(x) = -0.4x - 398398 = -0.4xx = -995There is only one maximum so the average value is -995

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