Question

The price in dollars of a TV is given by the equation p = (q^2/2400) + 1000, where q represents the demand for the product. Complete parts (a) through (d) below.

(a) What is the formula for the revenue function?

A. R(a) = p' * p

B. R(q) = q * p

C. R(q) = p' * q

D. R(q) = pq

(b) Find R(a).

(c) Find an expression equal to the marginal revenue. The marginal revenue is given by the expression:

(d) Find the marginal revenue when the demand is q = 20. The marginal revenue for q = 20 is

a. Find P(35), P(40), and P(85).

b. Find P'(35), P'(40), and P'(85).

c. Interpret your answers for parts a and b. Are there any limitations to this formula?

Answer 1

The formula for the revenue function is R(q) = q * p. To find R(a), substitute a for q in the revenue function. The marginal revenue is calculated by taking the derivative of the revenue function with respect to q.

Step-by-step explanation:

(a) What is the formula for the revenue function?

The correct formula for the revenue function is R(q) = q * p.

(b) Find R(a).

To find R(a), we need to substitute a for q in the revenue function:

R(a) = a * p

R(a) = a * [(a^2/2400) + 1000]

(c) Find an expression equal to the marginal revenue.

The marginal revenue is calculated by taking the derivative of the revenue function with respect to q. In this case, the derivative is:

R'(q) = p + q * p'

where p' is the derivative of p with respect to q.

(d) Find the marginal revenue when the demand is q = 20.

To find the marginal revenue when q = 20, substitute 20 for q in the expression for R'(q):

R'(20) = p + 20 * p'