$2.$ KON Ltd$.$ can produce the disk drive housings in the Hamilton, Ontario, plant at a rate of $150$ housings per month. Also, KON uses the drive housing at a fairly steady rate of $\backslash (\backslash$mathbf$\{720\}\backslash )$ per year. The housings cost $\backslash (\backslash$$ $85\backslash )$ each to produce, and the setup cost for beginning a production run is $\backslash (\backslash$$ $700\backslash ).$ The holding cost is assumed to be $\backslash (\backslash$mathbf$\{\backslash$$ $14.28\}\backslash ).($Apply EPQ model.$)$

$($a$)$ What is the optimal number of housings for KON to produce in each production run?

$($b$)$ Find $($i$)$ the time between initiation of production runs, $($ii$)$ the time devoted to production, and $($iii$)$ the setup time $($downtime$)$ each production cycle.

$($c$)$ What is the maximum dollar investment in housing that KON has at any point in time?