Question

If the price in dollars of a stereo system is given by

p (q )= 1000/q^2+ 1000



where q represents the demand for the product.



a. Find the marginal revenue when the demand is 10.


b. What is the formula for the revenue​ function?



a. R(q) = pq


b. R(q) = p'q


c. R(q) = p/q


d. R(q) = p'p

Answer 1

C.) R(q) = p/q

Explanation:

it's simple just divide those numbers by it's sign

Answer 2

a. The marginal revenue when the demand is 10 is -2.

b. The formula for the revenue​ function is a. R(q) = pq

How to find the marginal revenue

To find the marginal revenue when the demand is 10, differentiate the revenue function with respect to q and evaluate it at q = 10.

Given the price function:

p(q) = (1000/
`q^2`) + 1000

To find the marginal revenue, differentiate the price function with respect to q:

p'(q) = -2000/
`q^3`

Now, substitute q = 10 into the derivative to find the marginal revenue:

p'(10) = -2000/
`(10)^3`

p'(10) = -2000/1000

p'(10) = -2

Therefore, the marginal revenue when the demand is 10 is -2.

Regarding the formula for the revenue function, the correct option is:

a. R(q) = pq

The revenue function is obtained by multiplying the price (p) by the quantity demanded (q).

Therefore, the correct formula for the revenue function is R(q) = pq.