The private brewery produces monthly $4000$ hl of beer. $25\%$ of the production is

planned to be filled into glass bottles. The empty bottles are stored in plastic cases $($each case

contains $20$ bottles$)$ and the average annual holding cost per case is $20$ CZK$.$ The carrier,

transporting the cases into the brewery$$s store, charges a fixed cost associated with each order

for $11000$ CZK$.$ In addition, the brewery$$s own fixed cost of $1000$ CZK per each order is

necessary to be involved into the final calculation. The lead time between the placing each

order and its delivery is $1/2$ of month. Since filling of the bottles is the uniform process the

inventory depletion rate is uniform as well.

Management of the brewery decided to analyze the inventory system in order to minimize the

total cost associated with inventory replenishment and holding of the bottles in the store.

These questions should be answered:

$1.$ What is the optimum quantity order?

$2.$ What are the maximum level and the average level of inventory?

$3.$ What is the minimum total annual cost?

$4.$ When to order?

$5.$ How many orders are placed per year?