Question 1 - Inventory control methods (15 marks)

Pork Bellies is considering manufacturing ready-made meals in the new processing plant.The company is planning on working 250 working days per year and has devised the following estimates on sales of the new product:

Daily Sales

Probability

400

0.5

500

0.3

600

0.1

700

0.1

• The annual carrying cost per unit is $0.40
• Set-up time to manufacture the meals is 20 minutes for each of the 5 machines involved in preparing the meals and it costs $24.50 per hour for operators to set the machines up.
• Manufacturing overhead is charged out at a rate of $12.50 per machine hour.
• The ready-made meals are packaged in recyclable containers and cost $3.00 per 10 pack.The containers are sourced from Western Australia and can take anywhere between 15 to 20 days to arrive and have the following probability estimates:

Days to fill order

Probability

15

0.30

16

0.15

17

0.15

18

0.15

19

0.15

20

0.10

Required:

1. Calculate the economic size for each production run (3 marks)
2. When should an order for more containers be placed, based on expected values? (3 marks)
3. How can ordering be handled to eliminate stock-outs 9 out of 10 times without holding large amounts of containers? (4 marks)
4. Explain the differences in the basic philospophies underlying the JIT and EOQ approaches to inventory management (5 marks)

Question 2 - Linear programming (15 marks)

Pork Bellies has been approached by Hopewell Hospital, who coordinate meals for regional and city hospitals.Hopewell hospital who have devised a meal plan wants Pork Bellies to supply them with ready-made meals.Pork Bellies in consultation with Hopewell Hospital have devised a meal plan where 5 types of meals will be supplied based on calories and common allergies.The meals are:

1800C, 1500C, 800C, Gluten Free (GF) and Gluten and Dairy Free (GDF)

All meals go through the steps of food preparation, cooking and snap freezing.The time requirements per box of 20 meals is below as well as the available time, all in hours.

1800C

1500C

800C

GF

GDF

Selling Price ($)

15

14.5

13

15

13

Direct material

7

6.5

4

3

2

Direct labour

2

2

1.5

4

2

Variable overhead

1

0.5

1.5

0.5

0.5

Fixed overhead

2

2

2

2

2

Constraints:

1800C

1500C

800C

GF

GDF

Available (hours)

Mixing

1

0.5

0.5

1

1

1,500

Spreading

1

1

1

1

0.5

5,000

Cooking

0.5

1.5

2

0.5

0.5

2,300

Packaging

1

1

1

1

1

2,000

Due to the limits in the number of workers who may have access to the building at any one time because of COVID-19, a maximum of 100 1800C meals and a minimum of 50 GF meals for the month can be made.

Required:

1. Formulate a linear program to determine the expected mix of conference rooms to ensure the maximum profit will be created.Show all supporting calculations and solve using a computer package (eg solver in Excel) to derive the optimum solution. (5 marks)
2. Formulate a second linear programming taking into consideration the COVID-19 limitations. (3 marks)
3. State the optimal mix and resulting profit. Discuss your results (7 marks)

Question 3 - Correlation and regression (20 marks)

Pork Bellies is continuing to re-evaluate all aspects of the business and would like you to look into staffing costs.Below is a summary of the monthly costs.

Staff number

Number of meals

Staff cost ($)

January

20

700

27800

February

22

250

14000

March

10

200

12000

April

20

500

20000

May

24

650

23800

June

28

450

18400

July

16

50

20400

August

14

150

8200

September

24

350

18800

October

24

600

22200

November

16

300

16600

December

32

750

32200

The Pork Bellies relevant range has been estimated to be between 300 and 600 meals.

Required:

1. Draw a scatter diagram of Pork Bellies meals and staff costs and mark the relevant range (3 marks)
2. Use the high-low method to estimate the behaviour of Pork Bellies staff costs based on meal numbers within the relevant range.Use an equation to express the results of this estimation method. (3 marks)
3. Using excel or a similar program construct a regression analysis to estimate:
4. The equation to predict staff costs based on the number of meals within the relevant range (3 marks)
5. Based on the equation in 3 a) what would the staff cost be with 400 meals per month (2 marks)
6. Using both activities - number of meals and staff numbers, determine what the staff cost, within the relevant range, would be. (3 marks)
7. Does the inclusion of the additional cost driver (staff number) improve the model? Explain your answer (6 marks)
9. Question 4 (10 marks)
10. The Board of Directors would like your opinion on what strategic position Pork Bellies should now take reflecting on Case Study Part 1 and Case Study part 2.In your response consider short-term and long-term strategies the business may adopt.Include in your answer at least 2 options explaining how the strategy would be implemented and the likely outcome. (Maximum 500 words) (10 marks)