Question

The revenue (in thousands of dollars) from producing x units of an item is modeled by R(x)=12x-0.01x^2. a. Find the average rate of change in revenue as x changes from 1002 to 1007. b. Find the marginal revenue at x=1000.

Answer 1

It is given in the question that

The revenue (in thousands of dollars) from producing x units of an item is modeled by

$R(x)=12x-0.01x^2$

a. Average rate of change is given by

$\frac{R(1007)-R(1002)}{1007-1002}$

$= \frac{1943.51-1983.96}{5}$

$=\frac{-40.45}{5} = -8.09$

So the average rate of change of revenue is -8090dollars per unit .

b .To find the marginal revenue, we have to differentiate revenue function, that is

$R'(x)=12-0.02x$

And at x=1000, we will get

$R'(1000) = 12-0.02(1000)=-8$

S the marginal revenue is -8000 dollars.