# How many orders are placed annually?

Demand for a popular athletic shoe is nearly constant at 1500 pairs per week for a regional division of a national retailer. The cost per pair is \$48. It costs \$82 to place an order, and annual holding costs are charged at 22% of the cost per unit. The lead time is one week.
a. What is the EOQ?
b. What is the reorder point?
c. What is the cycle time?
d. What is the total annual cost?
2. Zip Games purchases blank DVD disks onto which it copies its software for sale through its mail order operation. A disk costs Zip \$.28. Processing an order for more disks cost \$15. Zip uses 60,000 disks annually, and the company has a 23% cost of capital.
a. Find the optimal order quantity.
b. How many orders are placed annually?
c. How frequently will orders be placed?
3. Kellam Images prints snack food bags on long rolls of plastic film. The plant operates 260 days a year. The daily production rate is 6200 bags, and the daily demand is 3600 bags. The cost to set up the design for printing is \$325. The holding cost is estimated at 2 cents per bag per year.
a. What is the recommended production lot size?
b. If there is a five-day lead time to set up the line, what is the recommended reorder point?
c. How long is each production run?
d. What is the TC for the recommended production plan?
e. Sketch the inventory level over time, including the highest inventory level, production run time, ?and cycle time.
4. The Tiernan Gallery and Art Museum distributes to its visitors a printed guide to its collections. There are about 17,000 visitors per year. Holding costs for the brochures are 21% and it costs \$28 to place an order with the printer. The printer has offered the following discount schedule:
Category Order Size Unit Cost
. 1 0 – 1499 \$2.50
. 2 1500 – 2999 \$2.20
. 3 3000 and over \$1.80
How many brochures should be printed at a time?

5. Bank Drugs sells Jami Michelle lipstick. The Jami Michelle Company offers a 6% discount on orders of at least 500 tubes, a 10% discount on orders of at least 1,000 tubes, a 12% discount on orders of at least 1,500 tubes and a 15% discount on orders at least 2,500 tubes.
Bank sells an average of 50 tubes of Jami Michelle lipstick weekly. The normal price paid by Bank drugs is \$1 per tube. If it costs Bank \$30 to place an order, and Bank’s annual holding cost rate is 26%, determine the optimal order policy for Bank Drugs.
6. The Fitness Shop is considering ordering a special model exercise machine. Each unit will cost the shop \$425 and it will sell for \$750. Any units not sold at the regular price will be sold at the year-end model clearance for \$360.
a. Assume that demand follows a normal probability distribution with m = 200 and s =35. What is ?the recommended order quantity?
b. Assume that demand is uniformly distributed between 100 and 300. What is the recommended ?order quantity?
7. Chez Paul Restaurant orders special Styrofoam “doggy bags” for its customers once a month and lead time is one week. Weekly demand for doggy bags is approximately normally distributed with an average of 120 bags and a standard deviation of 25 bags. Chez Paul wants at most a 3% chance of running out of doggy bags during the replenishment period. What is the reorder point for each of the orders? What is the safety stock in this case?
8. Amazing Bakers sells bread to 40 supermarkets. It costs Amazing \$1,250 per day to operate its plant. The profit per loaf of bread sold in the supermarket is \$0.25. Any unsold bread is returned to the Amazing Thrift Store to be sold at a loss of \$0.13.
a. If sales follow a normal distribution with ? = 70,000 and ??= 5,000 per day, how many loaves should Amazing bake daily?
b. Amazing is considering a different sales plan for which the profit per loaf of bread sold in the supermarket is \$.28 and the loss per loaf bread returned is \$.020. If ? = 62,000 and ??= 4,000 per day, how many loaves should Amazing bake daily?
9. Kelly’s Service Station does a large business in tune-ups. Demand has been averaging 220 spark plugs per week. Holding costs are \$.015 per plug per week and reorder costs are estimated at \$12 per order. ?Kelly does not want to be out of stock on more than 2% of his orders. There is a two-day delivery time. The standard deviation of demand is five plugs per day. Assume a normal distribution of demand during lead time and a 7-day work week.
a. What inventory policy do you suggest for Kelly’s station?
b. What is the average amount of safety stock for the reorder point in (a)?
c. What are the total variable weekly costs including safety stock costs?
10. The Academic Company mixes and bottles a high-energy beverage in various container types and sizes for college students. The aggregate forecast for the next four quarters in thousands of gallons is as follows:

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