As a manager at the local Hy$-$Vee, you learn that the store often experiences stockouts for Breakfast Blend Coffee. You suspect there might be a problem with inventory management, thus you decide to gather more data. The demand for Breakfast Blend Coffee turns out to be normally distributed. The mean demand for one week is $120$ packages and the standard deviation is $20$ packages. Hy$-$Vee's cost for Breakfast Blend coffee is $\backslash (\backslash$$ $3\mathrm{.}50\backslash )$ per package. The cost of carrying Breakfast Blend coffee in inventory is $\backslash (\backslash$$ $0\mathrm{.}50\backslash )$ per package per week. In addition, Hy$-$Vee incurs a cost of $\backslash (\backslash$$ $27\backslash )$ for placing an order and it takes $1$ week to receive the delivery.

a$.$ What is the Economic Order Quantity for Breakfast Blend Coffee? $(2$ points$)$

b$.$ For a continuous review system, what should be the reorder point and order quantity if Hy $-$Vee wants to provide a $\backslash (95\backslash \%\backslash )$ service level? Z values can be calculated in excel or using the table below. $(4$ points$)$

c$.$ No assume Hy$-$Vee reviews inventory every week and still wants to provide a $95\backslash \%$ service level. What should the inventory target be and how many units should be ordered? $(4$ points$)$

d$.$ Which inventory system $($continuous or periodic$)$ do you recommend for Breakfast Blend Coffee? Why? $(3$ points$)$

Table of z $-$values