Question $8$

$3$ pts

Kate's Mini$-$Mart uses a periodic review, order$-$up$-$to inventory model to manage inventory. For one of their more popular products, Tofu Jerky, Kate insists on using a $99\%$ fill rate target to set inventory levels. Kate buys Tofu Jerky for $$1\mathrm{.}00$ per pack and it sells for $$3\mathrm{.}50.$ It costs Kate $$0\mathrm{.}10$ per pack per week to hold inventory. The supplier has a $3$ week lead time $($with no randomness$).$ Average demand is expected to be $90$ per week. Standard deviation of forecast errors is expected to be $20.($Please use the Gamma distribution to model demand during the exposure period.$)$ Which statement best describes what will happen to inventory levels if Kate switches from ordering every week to ordering every three weeks?

Safety stock would decrease and cycle stock would decrease

Safety stock would decrease and cycle stock would increase

None of the above

Safety stock would increase and cycle stock would decrease

Safety stock would increase and cycle stock would increase