Question

Suppose that the revenue (in dollars) from the sale of a product is given by R = 50x + 0.9x2 − 0.004x3 where x is the number of units sold. How fast is the marginal revenue MR changing when x = 10?

Answer 1

The rate of change of the marginal revenue when x = 10 is found to be 1.56 dollars per unit, calculated by taking the second derivative of the revenue function and substituting x=10.

Step-by-step explanation:

The student's question centers on determining how fast the marginal revenue (MR) is changing for the given revenue equation R = 50x + 0.9x2 − 0.004x3 when x = 10. Marginal revenue is the derivative of the revenue function with respect to the number of units sold, so we need to calculate the derivative and then find its rate of change at x = 10.

First, let's find the derivative of the revenue function, which is:

MR = dR/dx = 50 + 1.8x - 0.012x2

Now, we determine the change in marginal revenue by finding the derivative of MR, which gives us:

dMR/dx = 1.8 - 0.024x

Finally, we substitute x = 10 into the equation to calculate the rate of change of marginal revenue:

dMR/dx at x = 10 = 1.8 - 0.024(10) = 1.8 - 0.24 = 1.56

The rate of change of the marginal revenue when x = 10 is 1.56 dollars per unit.