p = -0.059x + 250 (0 < or = x <or = 12000)?

Question

Pulsar also manufactures a series of 19-in color television sets. The quantity x of these sets demanded each week is related to the wholesale unit price p by the following function.
p = -0.059x + 250 (0 x 12000)
The weekly total cost incurred by Pulsar for producing x sets is represented by the following function.
C(x) = (0.000008)x3 - 0.01x2 + 470x + 73000
(a) Find the revenue function R.
R(x) =
Find the profit function P.
P(x) =

(b) Find the marginal cost function C'.
C '(x) =
Find the marginal revenue function R'.
R '(x) =
Find the marginal profit function P'.
P '(x) =

(c) Compute the following values. (Round your answers to 2 decimal places.)
C '(2900) =
R '(2900) =
P '(2900) =

Answer 1

The revenue is equal to the number of sets sold, times the unit price. So

R(x) = x*p(x) = -0.059x² + 250x

The profit is the revenue minus the total cost. So

P(x) = R(x) - C(x) = -0.059x² + 250x - [(0.000008)x³ - 0.01x² + 470x + 73000]
= -(0.000008)x³ - 0.049x² - 220x - 73000

Hmmm, there's a problem here. P(x) is negative for all positive values of x; that is, they would lose money no matter how many sets they sell.

I think you have a typo in C(x). If so, you should be able to fix up what I've written above.