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Mathematics with Modelling

07 Linear Programming

Group Presentation Assignment

Due Date: Thursday 2 November 2023, 11:30 AM

Group Presentation (10% of final grade)

· In your groups, you will create a hypothetical business that is trying to maximise income.

· You will need to make a group presentation showing the problem and the solution.

· Must be put in Powerpoint and then recorded to video format (eg on Teams).

· You will present your findings to the teacher by the group leader submitting a video (in .mp4) onto Teams Channel.

· Your group will also need to present your findings to the class. (Thurs & Fri)

· ALL members will need to participate in the presentation.

· The group leader will need to:

o Download the excel sheet and fill in the details of who is doing what

o Finalise time frame for jobs to be completed

o Make sure everyone is on track and doing their part  

o Put final video into your Teams Channel.

Decision Making Investigation:

In your groups decide on

· The group leader

· your company name

·  and the products your company will make

· Create a Powerpoint that fully explains your linear programming problem. Be colourful and clear. You can make a logo for your company.

Investigation:

This is what the boss of your company wants you to investigate:

 Do not change any of the values (highlighted) given already.

The [make up your own Company name eg Nike]_ company makes  [make up your own Product 1 eg Air Jordan 1]_  

and [make up your own Product 2 eg Air Jordan 4].

Each week the company must produce at least 12  [Product 1]_  but cannot produce more than 18.

Each week the company must produce at at least 25 [Product 2]_.

The   [Company name] company  can produce at most 80 [Product 1]_   and [Product 2] combined each week.

The company sells  [Product 1] for $[Price for Product 1]_   each and [Product 2]_   for $[Price for Product 2]_  each. (Note: here you can make up your own prices for Part 1, then different amount for Part 2 and compare with Part 1)  

Part 1

· How many of each item should be produced for a maximum weekly income?

· What is the maximum weekly income?

Part 2

· Discuss how the amount sold to maximise weekly income would change if one (or both) of the prices of the products sold, changes.

· Determine which option is the best to maximise weekly income ie compare answer in Part 1 and answer in Part 2.

Part 3

In particular, how would the prices need to change for more than one combination of products to give maximum income?

Be creative and as interesting as possible.

Your Powerpoint must include:

a. List of the important facts from your problem

b. Meaning for the variables

c. Give the Constraints

d. Give the Objective function

e. Graph with clearly labelled scale and axes (use Desmos or any other app to draw the graphs) and identify

f.  Vertices & objective function evaluation using tables or sliding line method

g. Solution.

h. At bottom of each slide state who produced slide and who is talking

 eg Min Lee ID  20712345

Note:

· Remember you are the company making a presentation. You are speaking to the boss (me) telling me what you should make and how much of it you should make, to maximise income ie clearly state which option gives maximum income.

· Do not speak only in mathematical terms.

· Explain how you came up with your equations.

· Make sure you explain what each line means and why it is relevant.

· Explain what your feasible region is and its relevancy.

· Again, you must speak in terms of the products being made not in terms of x and y.

· Check all the requirements for the Powerpoint.

· Make sure your cameras are ON when recording your video.

· Each slide in Powerpoint must indicate who produced slide and who is talking eg Min Lee ID  20712345

· Must submit everything onto Teams -> Assignments.  

Structure of Powerpoint

Slide 1 Title Slide

The first slide should state

• the topic

• the names of the group members (including ID numbers)

• You do not need to speak on this slide. Move to the next slide and start speaking.

Slide 2 – Introducing the Group

• The second slide introduces the group members to the audience.

• The Co-Ordinator will introduce each group member and start with the mihi: “Tēnā koutou, tēnā koutou, tēnā koutou katoa.”

Slide (3, 4, 5, ….)– Body   

The presentation should be divided into parts as follows.

1. Introduction

• Explain the purpose of the assignment

• Explain the type of decision that your group is helping the company to make  (looking at different possibilities for Objective functions ie compare Part 1 and Part 2  )

2. Identify feasible region, use diagrams(using Desmos or other drawing app), tables or any calculations

3. Use the results to make the decision

4. Look at other possibilities (eg Part 2 is like Part 1 but different costs)

5. Compare Part 1 and Part 2 and make a conclusion

6. Solve Part 3 and give conclusion

Final Slides – Personal Evaluation

• Each group member must record a personal evaluation on a separate slide at the end of the presentation. The evaluation (from each member) must answer these questions:

1. What was most difficult and challenging about the assessment?

2. What was most rewarding about the assessment?

3. What could be done to improve the assessment?

EACH PART should be PRESENTED BY A SEPARATE GROUP MEMBER.

THE part of the PRESENTATION (from new member speaking) he/she SHOULD START WITH THE MIHI: TĒNĀ KOUTOU, TĒNĀ KOUTOU, TĒNĀ KOUTOU KATOA.”

Formatting of Powerpoint

• Each slide must have a title

• Use the same font – Arial –

•  size 36 and bold for headings

•  size 24 or 28 for key words

• Limit the use of images. Use Unsplash or Pixabay to find suitable images that do not require attribution. Plagiarism will be penalised.

• Limit the use of animations. If you must choose ONE only and be consistent.

• Do not have different designs for each slide.

• Each group member is responsible for the formatting of the slides for their part of the assignment. The group leader must ensure consistency of presentation.

• At bottom of each slide that you made,  state your name and ID number.

Length of Presentation

• The video should be a maximum of 10 minutes long.

• Each part will vary in the number of slides:

• For example, Introducing members, Introduction of the assignment, Conclusion should only be one slide each.

Make the recording

 

 

Marking Schedule

 

How the marks given for the first 2 of the domains in the rubric:

Peer-review document given to each member of the group (that will be anonymous-no one in the group will know what you wrote) to identify how many marks can be given for  

· Roles and Responsibilities of each Individual

· Cooperation and Support