State the optimal mix and resulting profit. Discuss your results

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)