CR $=$

$0$

$1$

$2$

$3$

$0\mathrm{.}202$

$0\mathrm{.}159$

$0\mathrm{.}201$

$0\mathrm{.}125$

$4$

$0\mathrm{.}088$

$5$

$0\mathrm{.}087$

$6$

$0\mathrm{.}056$

$7$

$0\mathrm{.}025$

$8$

$0\mathrm{.}022$

$9$

$0\mathrm{.}018$

$10$

$0\mathrm{.}008$

$11$

$0\mathrm{.}006$

Faced with the demand for the perishable product of blood, hospital managers need to establish an ordering policy that deals

with the trade$-$off between shortage and wastage. As it turns out, this scenario, referred to as a single$-$period inventory

problem, is well known in the area of operations management, and there is an optimal policy. What we need to know is the

per$-$item cost of being short $($Cs$)$ and the per$-$item cost of being in excess $($CE$).$ In terms of the blood example, the hospital

estimates that for every bag short, there is a cost of $$80$ per bag, which includes expediting and emergency delivery costs.

Any transfusion blood bags left in excess at day's end are associated with a $$20$ per bag cost, which includes the original cost

of purchase along with end$-$of$-$day handling costs. With the objective of minimizing long$-$term average costs, the following

critical ratio, CR$,$ needs to be computed:

Cs

Cs $+$ CE

Recognize that CR will always be in the range of $0$ to $1.$ It turns out that the optimal number of items to order is the smallest

value of k such that P $($X k$)$ is at least the CR value.

Refer to the distribution of daily demand for blood bags $($X$).$

Bags used

Probability

$12$

$0\mathrm{.}003$

Based on the given values of Cs $=$ $$80$ and CE $=$ $$20,$ what is the value of CR$?$ Give your answer to one decimal place.

CR $=$