Each week, a computer store sells an average of $100$ sets of audio speakers. Weekly demand is normally distributed with a standard deviation of $4$ sets. The store orders speakers from a national distributor. Each order is filled in two weeks. The cost of placing each order is $$16,$ and the weekly cost of holding one set of speaker in inventory is $$2.$ The per$-$unit stockout cost is assumed to be $$4.$ The store is willing to assume that all demand is back$-$logged.

$($a$)(2)($b$)(4)($c$)(2)($d$)(2)$

$($e$)(4)($f$)(5)$

Determine a good size of order.

Determine a good reorder point.

What is the safety stock level?

If the new order is not always filled in one week, instead, the time for the new order to arrive has a mean of $1$ week and standard deviation of $1$ week. Determine a good size of order.

Continue part $($d$),$ determine a good reorder point.

If the weekly demand is increased from $100$ to $400,$ how will your answers in parts $($d$)$ and $($e$)$ change?

$0\mathrm{.}50\mathrm{.}550\mathrm{.}60\mathrm{.}650\mathrm{.}70\mathrm{.}750\mathrm{.}80\mathrm{.}850\mathrm{.}90\mathrm{.}950\mathrm{.}990\mathrm{.}999$

ZZ$\_\backslash$alphaZ$0\mathrm{.}00\mathrm{.}20\mathrm{.}40\mathrm{.}50\mathrm{.}60\mathrm{.}81\mathrm{.}02\mathrm{.}03\mathrm{.}04\mathrm{.}05\mathrm{.}06\mathrm{.}0$