HAL Ltd$.,$ discussed in Problem $9,$ can produce the disk drive housings in theHamilton, Ontario, plant at a rate of $150$ housings per month. The housings costHAL $$85$ each to produce, and the setup cost for beginning a production run is $$700.$Assume an annual interest rate of $28$ percent for determining the holding cost.a$.$What is the optimal number of housings for HAL to produce in each produc$-$tion run?G$($Q$*)$K$$Q$*$h$$Q$*2(50)(2,500)745(0\mathrm{.}45)(745)2335\mathrm{.}41.$Q$*$A$2$K$$h$.$nah$77856\_$ch$04.$qxd $1/9/083$:$21$ PM Page $219$nah$77856\_$ch$04.$indd $21917/12/146$:$39$ PM $220$ Chapter Four Inventory Control Subject to Known Demandb.Find the time between initiation of production runs, the time devoted to produc$-$tion, and the downtime each production cycle.c$.$What is the maximum dollar investment in housings that HAL has at any pointin time?