The SA trader has an average order of $50$ part that is processed in $8$ machines in their factory. And $20$ new orders are started in a through in a certain order monthly. There is $80\%$ for machine utilisation of which are operational at any time and $20\%$ are in repairs. The plant operates $160$ hours per month. And there is average of $7$ hours non$-$operation time per order in each machine.

However, the plant manager complains that a total of $100$ overtime machine$-$hours must be authorised each month to keep up with the production schedule.

$2\mathrm{.}1$ Determine the manufacturing lead time for an average order, if setup time takes $4$ hours, operating time for each part takes $15$ minutes and $25$ machine are at the factory.

$2\mathrm{.}2$ What is the plant capacity $($Hint: consider the useful information in question a$)?$

$2\mathrm{.}3$ In your own analysis, why must the overtime be authorised?