# Problem 1

Problem 1
The Bureau of Labor Statistics collects input and output data from various countries for comparison purposes. Labor hours are the standard measure of input. Calculate the output per hour from the following data. Which country is most productive?
Labor Hours Units of Output
United States 89.5 136
Germany 83.6 100
Japan 72.7 102

Problem 2.
Construct a network from the information in the following table and identify all the paths in the network, compute the length of each, and indicate the critical path. Determine the earliest start and finish times, latest start and finish times, and slack for each activity. Indicate how the critical path would be determined from this information.
Activity Activity Predecessor Time (weeks)
1 — 7
2 — 10
3 1 6
4 2 5
5 2 4
6 3, 4 3
7 5, 6 2
Problem 3.
Burger Doodle is a fast-food restaurant that processes an average of 680 food orders each day. The average cost of each order is \$6.15. Four percent of the orders are incorrect, and only 10% of the defective orders can be corrected with additional food items at an average cost of \$1.75. The remaining defective orders have to be thrown out.
a. Compute the average product cost.
b. In order to reduce the number of wrong orders, Burger Doodle is going to invest in a computerized ordering and cash register system. The cost of the system will increase the average order cost by \$0.05 and will reduce defective orders to 1%. What is the annual net effect of this quality improvement initiative?
c. What other indirect effects on quality might be realized by the new computerized order system?
Problem 4.
A firm is faced with the attractive situation in which it can obtain immediate delivery of an item it stocks for retail sale. The firm has therefore not bothered to order the item in any systematic way. However, recently profits have been squeezed due to increasing competitive pressures, and the firm has retained a management consultant to study its inventory management. The consultant has determined that the various costs associated with making an order for the item stocked are approximately \$70 per order. She has also determined that the costs of carrying the item in inventory amount to approximately \$27 per unit per year (primarily direct storage costs and forgone profit on investment in inventory). Demand for the item is reasonably constant over time, and the forecast is for 16,500 units per year. When an order is placed for the item, the entire order is immediately delivered to the firm by the supplier. The firm operates 6 days a week plus a few Sundays, or approximately 320 days per year. Determine the following:

a. Optimal order quantity per order
b. Total annual inventory costs
c. Optimal number of orders to place per year
d. Number of operating days between orders, based on the optimal ordering.

Problem 5.
The Commonwealth Banking Corporation issues a national credit card through its various bank branches in five southeastern states. The bank credit card business is highly competitive and interest rates do not vary substantially, so the company decided to attempt to retain its customers by improving customer service through a reduction in billing errors. The credit card division monitored its billing department process by taking daily samples of 200 customer bills for 30 days and checking their accuracy. The sample results are as follows:
Sample Number of Defectives Sample Number of Defectives
1 7 16 10
2 12 17 12
3 9 18 14
4 6 19 16
5 5 20 15
6 8 21 13
7 10 22 9
8 11 23 10
9 14 24 12
10 10 25 15
11 9 26 14
12 6 27 16
13 3 28 12
14 2 29 15
15 8 30 14

Develop a -chart for the billing process using control limits and indicate if the process is out of control.

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