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, we need to multiply the wholesale unit price p by the quantity demanded x. So, the revenue function R(x) = p * x.

To find the profit function P, we need to subtract the total cost function C(x) from the revenue function R(x). So, the profit function P(x) = R(x) - C(x).

To find the marginal cost function C', we need to find the derivative of the total cost function C(x) with respect to x. The marginal cost function represents the rate of change of the cost with respect to the quantity produced. So, C'(x) = dC(x)/dx.

To find the marginal revenue function R', we need to find the derivative of the revenue function R(x) with respect to x. The marginal revenue function represents the rate of change of the revenue with respect to the quantity sold. So, R'(x) = dR(x)/dx.

To find the marginal profit function P', we need to find the derivative of the profit function P(x) with respect to x. The marginal profit function represents the rate of change of the profit with respect to the quantity produced. So, P'(x) = dP(x)/dx.

Now, let's start solving these equations.

(a) Revenue function R:
R(x) = p * x

(b) Profit function P:
P(x) = R(x) - C(x)

(c) Marginal cost function C':
C'(x) = dC(x)/dx

(d) Marginal revenue function R':
R'(x) = dR(x)/dx

(e) Marginal profit function P':
P'(x) = dP(x)/dx

To compute the values at x = 1700, substitute x = 1700 into the corresponding functions and calculate the values.

C'(1700) = calculate C'(x) at x = 1700
R'(1700) = calculate R'(x) at x = 1700
P'(1700) = calculate P'(x) at x = 1700

Please provide the specific formulas for the total cost function C(x), the wholesale unit price p, and any other relevant information to proceed further with the calculations.