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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.

The revenue in thousands of dollars from producing x units of an item is modeled by Rx12x001x2 a Find the average rate of change in revenue as x changes from 10 class=

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It is given in the question that

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

[tex]R(x)=12x-0.01x^2[/tex]

a. Average rate of change is given by

[tex]\frac{R(1007)-R(1002)}{1007-1002}[/tex]

[tex]= \frac{1943.51-1983.96}{5}[/tex]

[tex]=\frac{-40.45}{5} = -8.09[/tex]

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

[tex]R'(x)=12-0.02x[/tex]

And at x=1000, we will get

[tex]R'(1000) = 12-0.02(1000)=-8[/tex]

S the marginal revenue is -8000 dollars.