Question

Both the average flow rate and average flow time of a process are increased by 50%, what will be the percentage change in the average number of units (inventory) in the process

(a) 125%
(b) 50%
(c) Cannot be determined
(d) 225%

Answer 1

From little's lawAverage inventory \(=\) average flow rate \(*\) average flow time

Initially let, inventory \(=\mathrm{I}\), average flow rate \(=\mathrm{R}\), average flow time \(=\mathrm{T}\)

Therefore, \(\mathrm{I}=\mathrm{R}^{*} \mathrm{~T}\)

Now, average flow rate and average flow time of a process are increased by \(50 \% .\)

Therefore, \(\mathrm{R}^{\prime}=\mathrm{R}+0.5 \mathrm{R}=1.5 \mathrm{R}\)

\(\mathrm{T}^{\prime}=\mathrm{T}+0.5 \mathrm{~T}=1.5 \mathrm{~T}\)

Therefore,

Inventory \(\left(I^{\prime}\right)=1.5 \mathrm{R}^{*} 1.5 \mathrm{~T}=2.25 \mathrm{RT}\)

Hence, percentage change in the average number of units (inventory) in the process,

\(\%\) change \(=\mathrm{I}^{\prime}-\mathrm{I}=2.25 \mathrm{RT}-\mathrm{RT}=1.25 \mathrm{RT}\) or \(125 \%\)

Thus, CORRECT ANSWER= (a) \(125 \%\)