Inventory control subject to known demand $(1)$

A food store considers importing a special kind of smoked sausages for sale. The store estimates that the demand is stable at $2100$ per year. The cost of placing an order and getting it delivered is $2000$ kr$.,$ and the cost of the sausages is $18\mathrm{.}50$ kr$.$ each. The store uses an annual internal interest rate of $22\%$ for the cost of capital. In addition, they operate with a storage cost of $3\%$ of the value of the item, and a cost of $2\%$ for taxes and insurance.

a$)$

What is the optimal order size of the sausages and how often should they be ordered?

b$)$

What is the ordering cost and the holding cost with this strategy?

c$)$

How many sausages should be in stock when a new order is placed if the lead$-$time is $3$ weeks?

d$)$

The market price for a sausage is estimated to $30$ kr$.$ What annual profit can the store expect on this product?

e$)$

The manager of the store realizes that the sausages will have a shelf life of $6$ weeks after they are delivered at the store. How will this affect the ordering strategy? What will the holding costs, the ordering costs and the profit be with this new assumption?

$2$