1. You need $50,000 cash throughout year. Your time is worth $100 per hour and it takes you a half-hour to get cash from your ATM. Your bank is paying 5% per annum passbook savings.
a. What is the EOQ?
b. What is the total cost at the EOQ?
c. How many times per year will you visit your ATM?

2. Consider the Economic Order Quantity Model. Prove algebraically that

a. , where TC* is the total inventory cost at the EOQ, and

b. , where TC* is the total inventory cost at the EOQ = Q*.

Remark: An algebraic proof involves working with the algebraic symbols, not with specific values of these symbols.

3. A small refrigeration shop stocks up on electric motors from a catalog supplier located in the Midwest. The price of the motors varies depending on the quantity purchased; the price breaks are shown in the table. The refrigeration shop knows it will need around 600 motors for the coming season and that it will cost them about $40 to place an order. Storage cost for the motors is based on i = 30%. In previous years they have bought all 600 at once and they are considering doing this again. What order quantity would you advise and how much can they save using your recommendation instead of their one order per year strategy? Note: The quantity discount applies to ALL units. For example, if you purchase 60 units, you pay $34.00 for all units from the first through the sixtieth for a total of $34 times 60 = $2,040.00.
Quantity Price/unit
1-49 $35.00
50-99 $34.00
100-499 $33.00
500 or more $30.00

4. The Union Street Microbrewery makes a beer, which it bottles and sells in its adjoining restaurant and by the case. It costs $1,000 to set up, brew, and bottle a batch of the beer. The annual cost to store the beer in inventory is based on i = 25% and C = $4.00 per bottle. The annual demand for the beer is 18,000 bottles and the brewery has the capacity to produce 30,000 bottles annually. Use the Uniform Lot Delivery model of page 393.
a. What is the optimal lot size?
b. What is the optimal annual cost?
c. What is the number of production runs a year?

5. Three Chums Fish Company buys fresh salmon daily from the fishermen that ply the deep waters of Puget Sound. Salmon are purchased for $2.50 per pound and sold to the public at $8.50 per pound. The salmon are kept fresh by displaying them on ice but at the end of the day, any unsold fish have a noticeable odor and are sold to a nearby chowder stand for $1 per pound. The past yearâ??s demand for salmon on Saturdays is shown in the table. Based on this information, what should their target service level and stocking point be? What is the significance of the target stocking level? Hint: See Chapter 12, Solved Problem 1, page 298.
Daily Demand (pounds) # Days at This Level
300 3
320 4
340 6
360 8
380 8
400 8
420 6
440 5
460 2