# Application of integration(the learning curve)

• Dec 17th 2011, 05:45 AM
Vinod
Application of integration(the learning curve)
The production manager of an electronic company obtained the following function
$\displaystyle f(x)=1356.4x^{-0.3218}$

Where f(x) is the rate of labour hours required to assemble the $\displaystyle x^{th}$ unit of a product. The function is based on the experience of assembling the first 50 units of the product. The company was asked to bid on a new order of 100 additional units.
find the total labour hours required to assemble 100 units

SOLUTION: -

N=$\displaystyle \int_{50}^{150}f(x)dx=\int_{50}^{150}1356.4x^{-0.3218}$

N=$\displaystyle \left|\frac{1356.4x^{0.6782}}{0.6782}\right|_{50}^ {150}$

N=$\displaystyle 2000\left|150^{0.6782}-50^{0.6782}\right|$

Using logarithm and anti-logarithm,we get,

N=$\displaystyle 2000[29.91-14.2]$

N=31420

Hence company can bid estimating the total labour hours needed 31420

If I am wrong in finding the solution, reply me.
• Dec 17th 2011, 09:10 AM
ILikeSerena
Re: Application of integration(the learning curve)
Hi Vinod! :)

I do wonder though, whether you're supposed to make a continuity correction.
This would mean adding 0.5 to both integral boundaries.
Or is this out of scope of your material?

This may be nitpicking, but are you supposed to do that?
• Dec 18th 2011, 03:32 AM
Vinod
Re: Application of integration(the learning curve)
Quote:

Originally Posted by ILikeSerena
Hi Vinod! :)