Question

The manager of a CD store has found that if the price of a CD is p(x) = 69 - (6/x), then find the number of CDs that will produce maximum revenue. What is the expression for total revenue from the sale of x CDs?

Option 1: R(x) = 69x - 6
Option 2: R(x) = 69 - 6x
Option 3: R(x) = 69x - 6/x
Option 4: R(x) = 69 - x/6

Answer 1

To find the number of CDs that will produce maximum revenue, we can use the revenue function R(x) = x * p(x), where p(x) is the price function. By substituting the given price function p(x) = 69 - 6/x into the revenue function, we can simplify the expression and find that the total revenue from the sale of x CDs is R(x) = 69x - 6.

Step-by-step explanation:

To find the number of CDs that will produce maximum revenue, we need to maximize the revenue function R(x).

The revenue from selling x CDs is given by the equation R(x) = x * p(x), where p(x) is the price function.

Substituting the given price function p(x) = 69 - 6/x, we get R(x) = x * (69 - 6/x).

To simplify the expression, we can multiply out the brackets to get R(x) = 69x - 6.

Therefore, the expression for total revenue from the sale of x CDs is R(x) = 69x - 6.