Question 1 Scenario: The owner of a large bicycle sales and repair business stoc

ID: 3581299 • Letter: Q

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Question 1

Scenario: The owner of a large bicycle sales and repair business stocks a popular brand of mountain bikes. Based on historical data, the estimated annual demand for the bikes is 1375 units. The estimated average demand per day is 11 units. The purchase cost from the distributor is $765.00 per unit. The lead-time for a new order is 7 days. The ordering cost is $72.50 per order. The average holding cost per unit per year is $32.51. The business has traditionally ordered 48 units each time they placed an order. Based upon using the businesses’ current ordering model:

The owner of a bicycle repair and sales business has hired you to help him make his business more profitable. The following table shows sales data for one product for each month for the year (assume 30 days/month). These data will be referenced in order to answer questions 1 - 18.

Month

Sales

Forecast

Month 1

Month 2

Month 3

Month 4

Month 5

Month 6

Month 7

Month 8

Month 9

Month 10

Month 11

Month 12

Month 13

Question 1: Use a 4-month moving average to calculate the sales forecast for months 5, 10 & 13.

77.25, 79.25 & 77.00

77.50, 79.75 & 76.75

78.75, 81.00 & 78.25

81.50, 81.00 & 75.50

Question 2

Question 2: Refer to the data in the Question 1 and use exponential smoothing at an alpha of 0.30 to calculate each month’s forecast. What are the forecasts for Months 4, 10 & 12?

83.92, 80.08 & 76.14

80.92, 77.74 & 76.82

80.71, 77.16 & 76.84

81.97, 79.28 & 79.38

Question 3

Question 3: Refer to the data in the Question 1 and calculate the seasonal index for Months 3 and 6.

0.85 & 1.08

0.85 & 1.09

0.87 & 1.03

0.83 & 1.06

Question 4

Question 4: Refer to the data in the Question 1 and use the forecast generated by the exponential smoothing method to calculate the MAD for the data.

9.29

8.85

8.19

7.37

Question 5

Question 5: Refer to the data in the Question 1 and calculate the Weighted Average Forecast for Months 5 - 13 where the most recent month carries a weight of 4, the next most recent month a weight of 3, the next a weight of 2 and finally the oldest month carries a weight of 1. The weights are arranged from the most recent month to the oldest month: 4, 3, 2, & 1. What are the forecasts for months 6, 9 & 13?

71.2, 79.4 & 79.2

73.7, 81.9 & 81.0

75.3, 80.5 & 77.0

70.3, 78.4 & 79.5

Question 6

Question 6: Refer to the data in the Question 1. What is the average number of units in inventory based upon ordering 48 units each time an order is placed?

31.0

32.0

27.5

24.0

Question 7

Question 7: Refer to the data in the Question 1. How many orders per year will be necessary based upon ordering 48 units each time an order is placed? Round your answer to two decimals.

20.70

22.73

28.65

20.81

Question 8

Refer to the data in the Scenario 1 for Question 1. What is the average dollar value of inventory based upon ordering 48 units each time an order is placed? (Rounded to the nearest dollar)

$18,360

$22,165

$18,838

$22,720

Question 9

Question 9: Refer to the data in the Question 1. What is the total annual cost (Purchase Cost + Ordering Cost + Holding Cost) based upon ordering 48 units each time an order is placed? (Rounded to the nearest dollar)

$858,689

$924,547

$1,054,732

$943,100

Question 10

Question 10: Refer to the data in the Question 1. What is the optimal reorder point based upon ordering 48 units each time an order is placed?

Question 11

Scenario: The president of the bicycle business has recently heard about the EOQ model and is interested in learning whether or not using this model would allow the company to reduce its annual costs by optimizing the number of orders placed each year and the number of bicycles purchased in each order. The estimated annual demand for the bicycles, estimated average demand per day, purchase cost from the bicycle manufacturer per unit, lead time for a new order, ordering cost per order and average holding cost per unit per year remain the same as stated in the scenario for the current ordering model. Based upon using the EOQ model (with instantaneous receipt):

Question 11: What is the economic order quantity (EOQ) that will minimize inventory costs?

64.64

75.35

78.31

78.97

Question 12

Question 12: Refer to the data in the Question 11. How many orders per year will be necessary based upon using the EOQ?

19.96

16.59

16.78

17.56

Question 13

Question 13: Refer to the data in the Question 11. What is the average number of units in inventory based upon ordering using the EOQ?

37.67

39.15

39.48

32.32

Question 14

Question 14: Refer to the data in the Question 11. What is the average dollar value of inventory based upon ordering using the EOQ? (Rounded to the nearest dollar)

$23,108

$25,806

$28,033

$29,953

Question 15

Question 15: Refer to the data in the Question 11. What is the total annual cost (Purchase Cost + Ordering Cost + Holding Cost) based upon using the EOQ? (Rounded to the nearest dollar)

$858,573

$943,049

$1,054,421

$924,545

Question 16

Question 16: Refer to the data in the Question 11. What is the optimal reorder point based upon using the EOQ?

Question 17

Scenario: The bicycle distributor has proposed a quantity discount schedule for mountain bikes as reflected in the following table for consideration by the president as a means to potentially reduce his total annual costs.

Discount Number

Quantity Ordered

Unit Cost Discount

0 to 60

61 to 80

18%

81 and over

20.25%

The estimated annual demand for the bicycles, estimated average demand per day, purchase cost from the bicycle distributor per unit, lead time for a new order, ordering cost per order and average holding cost per unit per year remain the same as stated in the scenario for the current ordering model. Based upon using the quantity discount model:

Question 17: What order quantity will allow the wholesale distributor to minimize total annual inventory costs (Purchase Cost + Ordering Cost + Holding Cost) by taking advantage of the proposed discount pricing?

101

Question 18

Question 18: Refer to the data in the Question 17. What is the total annual cost (Purchase Cost + Ordering Cost + Holding Cost) based upon taking advantage of the proposed discount pricing? (Rounded to the nearest dollar)

$753,816

$699,941

$766,452

$841,167

Question 19

Scenario: The owner of the business stocks two types of bicycle oil: conventional and synthetic. His storeroom has room for no more than 95 cans of oil in stock. A review of his sales history suggests that at least 2.5 times as much conventional oil is sold as synthetic. Additionally experience has shown him that, due to demand, he should keep a maximum of 40 cans of conventional oil but have no less than 30 cans on hand. Experience has shown that demand for synthetic oil is somewhat unpredictable therefore he thinks he should keep a minimum of 15 cans of the synthetic in stock. He purchases the conventional oil for $4.50 per can and the synthetic oil for $5.75 and sells them for $5.50 and $7.50 respectively.

Question 19: How many cans of conventional oil should he stock in his center in order to make the maximum profit? Round down your answer to the nearest whole can.

Question 20

Refer to the data in the Scenario for Question 19. How many cans of synthetic oil should he stock in his center in order to make the maximum profit? Round down your answer to the nearest whole can.

Question 21

Refer to the data in the Scenario for Question 19. Using the rounded values for Questions 19 & 20 calculate the maximum profit.

$45.00

$65.00

$66.95

$68.25

Question 22

Scenario: The bicycle center also sells new bikes. He purchases three types of bicycles from manufacturers in kit form, then assembles, services & inspects them prior to sale. The assembly of mountain bikes requires 3.25 hours, cross-country bikes require 2.15 hours and three-wheelers require 3.85 hours of labor. Servicing mountain bikes requires 2.75 hours, cross-country bikes require 1.75 hours and three-wheelers require 4.50 hours of labor. The inspection & testing of mountain bikes requires 3.25 hours, cross-country bikes require 3.15 hours and three-wheelers require 4.25 hours of labor. The center makes a profit of $165.00 on each mountain bike, $140.50 on cross-country bikes and $265.75 on each three-wheeler. The center has 180 assembly hours, 220 service hours and 260 inspection & testing man-hours available. Because spring is just around the corner the center decides that it is best if ten mountain bikes and twelve cross-country bikes are assembled and stocked ready for sale.

Question 22: How many mountain bikes should he assemble & stock in his center in order to make the maximum profit? Round down your answer to the nearest whole bike.

Question 23

Refer to the data in the Scenario for Question 22. How many cross-country bikes should he assemble & stock in his center in order to make the maximum profit? Round down your answer to the nearest whole bike.

Question 24

Refer to the data in the Scenario for Question 22. How many three-wheeler bikes should he assemble & stock in his center in order to make the maximum profit? Round down your answer to the nearest whole bike.

Question 25

Refer to the data in the Scenario for Question 22. Using the rounded values for Questions 22 - 24 calculate the maximum profit?

$7,746.75

$11,574.25

$12,584.25

$8,171.75

Question 26

Scenario: The owner of the bike shop realized that according to the control charts the method used by his mechanics to fill and check the air pressure in mountain bike tires needed some revision. Therefore he decided to break down the procedure into eight activities and construct a PERT Diagram. After running the data (shown in the table below) Identify the Critical Path.

Activity

A, B, F & G

A, C, D, F & G

A, B, D, F & G

A, B, D, F, G & H

Month

Sales

Forecast

Month 1

Month 2

Month 3

Month 4

Month 5

Month 6

Month 7

Month 8

Month 9

Month 10

Month 11

Month 12

Month 13

Explanation / Answer

1. 81.50, 81.00 & 75.50

2. 83.92, 80.08 & 76.14

3. 0.87 & 1.03

4. 7.37

5. 75.3, 80.5 & 77.0

6. 31.0

7. 28. 65

8. $18,36 0

9. $1,054,73 2

10. 6 6

11. 64.64

12. 16.5 9

13. 37. 67

14. $25,80 6

15. $25,80 6

16. 5 4

17. 81

18. $841,167

19. 15

20. 20

21. $65.00

22. 10

23. 12

24. 31

25. $12,584.25

26. A, B, D, F & G

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