The weekly demand for the Pulsar 25 color LED television is represented by p, where p denotes the wholesale unit price in dollars and x denotes the quantity demanded.


The weekly total cost function associated with manufacturing the Pulsar 25 is given by C(x), where C(x) denotes the total cost incurred in producing x sets.


(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 two decimal places.)

C '(1700)
=

R '(1700)
=

P '(1700)
=

To find the revenue function R, you need to multiply the quantity demanded (x) by the wholesale unit price (p). Since the wholesale unit price is denoted by p, the revenue function R(x) is given by:

R(x) = p * x

To find the profit function P, you need to subtract the total cost function C(x) from the revenue function R(x):

P(x) = R(x) - C(x)

To find the marginal cost function C ', you need to take the derivative of the total cost function C(x) with respect to x. The marginal cost function is denoted as C ' (x).

To find the marginal revenue function R ', you need to take the derivative of the revenue function R(x) with respect to x. The marginal revenue function is denoted as R ' (x).

To find the marginal profit function P ', you need to take the derivative of the profit function P(x) with respect to x. The marginal profit function is denoted as P ' (x).

To compute the values C '(1700), R '(1700), and P '(1700), substitute x = 1700 into the corresponding marginal cost, marginal revenue, and marginal profit functions.

It is important to note that the specific equations for the total cost, revenue, and profit functions were not provided in the question. In order to provide a complete answer, we would need these equations.