Question

The company Robots for you, Inc. manufactures robots that help with household tasks. The revenue from the sale for their robot model MYT597 is given by R(x)=450x+540(5x+2)−1−300 where x is the number of units sold.

a) Determine the corresponding marginal revenue
b) The marginal revenue, rounded to 2 decimal places, when 90 units of robot model MYT597 are sold is
c) If 94 units of robot model MYT597 are sold, find an approximation to how much the revenue will change, rounded to 2 decimal places

Answer 1

The revenue function for the robot model MYT597 is given as R(x) = 450x + 540(5x + 2)^{-1} - 300. To find the marginal revenue, calculate the derivative of the revenue function. Substitute the given value of x to find the marginal revenue when 90 units are sold. To approximate the change in revenue, subtract the revenue when 94 units are sold from the revenue when 90 units are sold.

Step-by-step explanation:

The revenue function for the robot model MYT597 is given as:

R(x) = 450x + 540(5x + 2)^{-1} - 300

To find the marginal revenue, we need to calculate the derivative of the revenue function with respect to x:

R'(x) = 450 - 540(5x + 2)^{-2}(5)

Now substitute x = 90 into the derivative equation to find the marginal revenue when 90 units are sold:

R'(90) = 450 - 540(5(90) + 2)^{-2}(5)

Finally, to approximate how much the revenue will change if 94 units are sold, we can subtract the revenue when 94 units are sold from the revenue when 90 units are sold:

R(94) - R(90)