1)  The office manager of a legal firm is responsible for ordering copier paper to supply all of the copiers located on the firm's six floors.  The machines require a total of 22 boxes of paper each day, 6 days per week, 52 weeks per year.  The paper is ordered from a large distributor at a rate of $12 per box.  The distributor also bills the firm a $20 fulfillment charge for each order placed and levies a freight charge for shipping.  Paper is shipped in cases of one dozen boxes, and the distributor determines the shipping cost to the customer at a rate of $24 per case.  Every time the firm orders paper it requires a clerk, paid at the rate of $10 per hour, 30 minutes to generate and distribute the appropriate paperwork.  Since there is not enough room on the premises for storage alternate space is contracted from another tenant in the building.  The tenant charges the firm a flat $2.80 for every box of paper he holds in inventory for a year.  All of the firm's purchases are financed at 1 and 1/2% per month, and no shortages of any office supplies are allowed.

a)  Currently the firm orders 100 boxes of paper at a time.  What is the total relevant cost of this policy?

b)  How many boxes should the firm order under an optimal policy?

c)  What is the total relevant cost of the optimal policy?

d)  How many orders are placed each year under the optimal policy?

e) How many days are there between orders under the optimal policy?

Suppose the partners of the firm inform the office manager that they consider the cost of carrying inventory too expensive.  They suggest that with some supplies, such as copier paper, occassional shortages could be tolerated.  Any prints jobs that might be interrupted could be run when the new paper order is received.  One of the partners, specializing in economics, acknowledges that, while he could see no direct negative impact of such shortages on revenues to the firm, there may be an opportunity cost of some kind.  He confidently informs the office manager that an appropriate penalty cost would be $2 for each box of paper short.

f)  How many boxes should the firm order under the new optimal policy?

g)  What is the total relevant cost of the new optimal policy?

h)  How many boxes of each new delivery will be set aside to run accumulated print jobs?

i)  What percentage of the time is the firm out of copier paper stock?

After a few weeks under the new policy another partner approaches the office manager to explain that the policy was not acceptable.  She is worried about the health of the firm and insists that they be out of copier paper stock no more than 5% of the time.

j)  What is the imputed penalty charge?

k)  What is the total relevant cost of the newest optimal policy?

2)   Acme steel mill can produce 5,000 tons of steel per week, 52 weeks per year.  They have orders for 15,000 tons of steel per month, 12 months per year.  Each ton of steel costs $600 for raw materials and $1,200 to refine and produce.  All inventories are valued at an internal rate of return of 20%, and every time the blast furnace is restarted it costs Acme $10,000.

a)  How much steel should be produced in a single production run?

b)  How many days does a production run last?

c)  How many days pass between times the blast furnace is restarted?

d)  What is the maximum inventory on hand?

e)  What is the total relevant cost of the optimal policy?

3)  DigiTech, a small personal computer maker, buys high definition color monitors from a high-end supplier.  The cost per unit is determined by the following guidelines:
 

DigiTech has an annual demand for 730 custom computers.  Every time the company orders monitors it incurs a cost of $20, and it calculates that every monitor held in inventory for a year costs the firm $50.

a)  Without considering quantity discounts what is the economic order quantity?

b)  Taking quantity discounts into consideration what is the economic order quantity?

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