Expert: Paul Klarreich - 5/5/2007

Question
Suppose that a company's maginal revenue from the manufacture of egg beaters is dr/dx = 2-2/(x + 1), where r is measureed in thousands of dollars and x in thousands of unitss. How much money should the company expect from a production run of x = 3 thousand egg beaters? To find out, integrate the marginal revenue from x=0 to x=3

Answer
Questioner:   zagas
Category:  Calculus
Question:  Suppose that a company's maginal revenue from the manufacture of egg beaters is dr/dx = 2-2/(x + 1), where r is measureed in thousands of dollars and x in thousands of units. How much money should the company expect from a production run of x = 3 thousand egg beaters? To find out, integrate the marginal revenue from x=0 to x=3
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Hi, Zagas,

If all you need is the integration, that shouldn't be too bad:

*************** VIEW IN COURIER FONT ***********

{3         2
|   [2 - ----- ] dx =
}0       x + 1  


2x - 2 ln(x + 1), from  x = 0 to x = 2

[2(2) - 2 ln(2 + 1) ] - [ 2(0) - 2 ln(0 + 1) ] =

[4 - 2 ln(3) ] - [ 0 - 2 ln(1) ] =

[4 - ln(9) ] - [ 0 - 2(0)] =

4 - ln 9 =  Well, you can use your calculator for this.

Mine gives:   1.802775,
which, I suppose, means  $1802.775