Question

Suppose the revenue (in dollars) from the sale of x units of a product is given by R(x) = (24x² + 38x) / (2x + 2). Find the marginal revenue when 23 units are sold.

Answer 1

The marginal revenue when 23 units are sold is obtained by deriving the revenue function R(x) and evaluating it at x = 23, after simplifying the resulting expression.

Step-by-step explanation:

To find the marginal revenue when 23 units are sold, we need to first determine the derivative of the revenue function R(x), because the derivative represents the rate of change of revenue with respect to the number of units sold, which is the definition of marginal revenue. The given revenue function R(x) is (24x² + 38x) / (2x + 2). Let's calculate its derivative:

1. Calculate the derivative of the numerator, which is 48x + 38.
2. Calculate the derivative of the denominator, which is 2.
3. Apply the quotient rule for derivatives, which is (v'*u - u'*v) / v², where u is the numerator and v the denominator. Here, R'(x) = [(2)(48x + 38) - (24x² + 38x)(2)] / (2x + 2)².
4. Simplify the result to get R'(x) in terms of x.
5. Substitute x = 23 into R'(x) to find the marginal revenue for when 23 units are sold.