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

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