1. Demand for a product is 12 units a day, 360 days a year. The product can be ordered for 20/cents unit. The shipping cost of the order is $8 no matter what the order size is and it takes a week for an order to arrive. The backlog cost is estimated at $6 per unit per year and there is a 20% per year as a rate of return to estimate the inventory carrying cost.

a. How many units should be ordered at a time?

b. When should the order be placed based on the inventory position?

c. What is the total annual cost of meeting demand for this product?

2. A company can package their own item or buy pre-packed item. If they package their own , there is a production setup cost of $20. The unit production cost is $1.23 per item, and the production rate is 500 items/day. Pre-packed  items cost the company $1.26 per item and the fixed ordering cost is $3 per order. For either, there is a 24% per year rate of return to calculate the inventory carrying charge. Demand for item is 10,000 items per year.

a. what is the EOQ?

b. what is the EPQ?

c. From cost stand point, what should the company do?

d. What other considerations might affect the decision?

3. A company produces filters for domestic and foreign cars. One filter is supplied on an exclusive contract basis at a constant 200 units monthly. The company can produce this filter at a rate of 50 per hour. Setup time to change the settings on the equipment is 1.5 hrs. Worker time (including overhead) is charged at the rate of $55 per hour, and the plant idle time during the setups is estimated to cost the firm $100 per hour. There is a 22% annual interest rate for determining holding cost. Each filter costs the company $2.50 per unit to produce. Assuming 6-hour days, 20 working days a month, and 12 months a year:

a. How many filters should they produce in each production run to minimize annual holding and setup costs?

b. Assuming that it produces the optimal batch size, what's the maximum inventory level ?

c. What is the % of run-time?