The revenue from the sale of x units of a product is represented by the following formula.
R = 10(5x + 1)–1 + 70x – 11 dollars
Find the marginal revenue when 50 units are sold. (Round your answer to the nearest cent.)
To find the marginal revenue when 50 units are sold, we need to calculate the derivative of the revenue function with respect to the number of units sold (x), and then substitute x = 50 into that derivative equation.
Step 1: Finding the derivative of the revenue function
The revenue function is given by R = 10(5x + 1)^-1 + 70x - 11 dollars.
To find the derivative, we will apply the power rule and product rule:
dR/dx = 10(-1)(5x + 1)^(-2)*d(5x + 1)/dx + 70
= -10(5x + 1)^(-2)*5 + 70
Simplifying further:
dR/dx = -50/(5x + 1)^2 + 70
Step 2: Substitute x = 50 into the derivative equation
We need to substitute x = 50 into the derivative equation we found in Step 1.
dR/dx = -50/(5(50) + 1)^2 + 70
= -50/251^2 + 70
Simplifying further:
dR/dx = -0.1594 + 70
= 69.8406
Step 3: Round the answer to the nearest cent
The marginal revenue when 50 units are sold is approximately $69.84 (rounded to the nearest cent).