$1.$ A firm orders $2500$ units of a part each year from a supplier. The holding cost for this part is

$$50$ per unit per year. The ordering cost is $$100$ per order. Based on this, find the following:

a$.$ Determine economic order quantity.

b$.$ Compute the total annual cost of carrying and ordering inventory, assuming the EOQ value is

used for quantity.

c$.$ Compute the number of orders per year.

$2.$ The Pen&Pencil Shop is a producer of pencils. The annual demand for pencils is $15,000$ units.

Pencils can be produced at a rate of $200$ per day, and the usage rate is $50$ units per day. The

annual storage cost is $$2$ per pencil, and the machine setup cost is $$50$ per run.

a$.$ Determine the economic run quantity.

b$.$ How many runs per year will there be$?$

c$.$ Compute maximum inventory level.

d$.$ Compute total annual cost, assuming the economic run quantity is used for quantity.