Problem $3$: Using the original sales data from problem $2.$

a$)$ Use exponential smoothing with a $=0\mathrm{.}6$ to forecast the sales for the month April through December. Assume that the initial forecast for January was $$3,200.$

b$)$ What is the forecast for the $2^{nd}$ January?

Problem $4$: Sam's Pet Hotel operates $52$ weeks per year, $6$ days per week. It purchases kitty litter for $$11\mathrm{.}70$ per bag. The following information is available about these bags.

Demand $=90$ bags $\frac{?}{?}$ week

Order Cost $=$$$\frac{54}{?}$ order

Annual holding cost $=27\%$ of cost

a$.$ What is the EOQ?

b$.$ What is the average time between orders $($in weeks$)?$

c$.$ The store currently uses a lot size of $500$ bags $($ie$.Q=500).$ What is the annual holding costs of this policy? Annual ordering cost? Without calculating the EOQ, how can you conclude from these two calculations that the current lot size is too large?

d$.$ What would be the annual cost saved by shifting from the $500-$ bag lot size to the EOQ?

Problem $5$: Inventory records show the following. Complete an ABC Analysis $($make sure to clearly indicate which Series letters are $A,B$ or C $.$

$\backslash$table$[[$Series$,$Unit Cost,Count$],[$Q$,$$$34\mathrm{.}23,17],[$R$,$$$462\mathrm{.}00,22],[$S$,$$$96\mathrm{.}42,24],[$T$,$$$88\mathrm{.}44,63],[$U$,$$$1,751\mathrm{.}34,6],[$V$,$$$38\mathrm{.}04,51],[$W$,$$$382\mathrm{.}73,14]]$