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$\textbf{Consider two cases as below.}$
$\textbf{Case 1:}$ A company buys $1000$ pieces per year of a certain part from vendor $’X’.$
The changeover time is $2$ hours and the price is $Rs.\: 10$ per piece. The holding cost rate per part is $10\%$ per year.
$\textbf{Case 2:}$ For the same part, another vendor $’Y’$ offers a design where the changeover time is $6$ minutes, with a price of $Rs 5$ per piece, and a holding cost rate per part of $100\%$ per year. The order size is $800$ pieces per year from $’X’$ and $200$ pieces per year from $’Y’$.
Assume the cost of downtime as $Rs.\:200$ per hour. The percentage reduction in the annual cost of $\text{Case 2}$, as compared to $\text{Case 1}$ is __________ (round off to $2$ decimal places).
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