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3.2 AS91574
In this standard you will need to:
In this standard you will need to:
1. Read the question/context carefully and form a number of inequalities in 2 variables to be solved simultaneously;
1. Read the question/context carefully and form a number of inequalities in 2 variables to be solved simultaneously;
2. Graph the entire system of inequalities onto desmos accurately (stating whether you are shading in or shading out);
2. Graph the entire system of inequalities onto desmos accurately (stating whether you are shading in or shading out);
3. Identify the feasible region and its vertices;
3. Identify the feasible region and its vertices;
4. Decide which of the vertices of the feasible region give the optimal solution by either the sliding rule method (deeper understanding for E) or vertex method;
4. Decide which of the vertices of the feasible region give the optimal solution by either the sliding rule method (deeper understanding for E) or vertex method;
5. State the optimal solution to the problem in context.
5. State the optimal solution to the problem in context.
...and for Excellence...
6. Explain the effect of a change to the context, find multiple solutions to a problem or investigate integer requirements to solutions
6. Explain the effect of a change to the context, find multiple solutions to a problem or investigate integer requirements to solutions
Work through the steps below to master the technique!
Work through the steps below to master the technique!
1: Understanding what Linear Programming is.
1: Understanding what Linear Programming is.
In this section you need to watch the videos carefully and get an overview of the topic. There will not be much need to write too many notes I wouldn't think.
Understanding what is meant by the term 'Optimisation' - https://www.youtube.com/watch?v=Uo6aRV-mbeg
2: Forming constraints from words into inequalities
2: Forming constraints from words into inequalities
Forming constraints from words into Inequalities is a key part of linear programming. Watch the videos below, take notes and then practice for yourself using the questions to the right.
This video follows from the previous introduction and takes you through how to form inequalities from worded situations - https://www.youtube.com/watch?v=uJFiR0DG2Bw
Another explanation here: https://youtu.be/vCKJkKBLYdQ
This link starts at the real basics for those rusty from Year 10! - https://www.youtube.com/watch?v=JQZt85V6zlo
This video starts the graphing process below too: https://www.youtube.com/watch?v=cL9Hl9rrgm0
3: Graphing the constraints and labelling the feasible region.
3: Graphing the constraints and labelling the feasible region.
Once you have some equations that describe the situation you can graph them so you can see the problem visually. Do the questions on the right to get to grips with htis idea. - You may like to experiment with using desmos to do this too!
https://www.youtube.com/watch?v=wKRU1boorUk&list=PLZocUikpczs92VbQSc2yt8A2QDFwc8972&index=1
4: Forming the optimal function and finding optimal solutions.
4: Forming the optimal function and finding optimal solutions.
We will be using desmos but its pretty similar.
You may also like to watch the Machine Parts video too also in his playlist.
Use this tutorail to help you to use desmos to graph the inequalities like in the video
Summary
Summary
Worked examples as far as Merit
Worked examples as far as Merit
Worked example of basic process (Washer/Dryer eg) washer/dryer example in desmos
Try one for yourself!
Try one for yourself!
Infinite Randomised Question generator :)
Infinite Randomised Question generator :)
Use this link to open a new window on a site which randomly generates an endless supply of questions. Only one type of Excellence question repeated over and over again but a good way to get started! (if the link doesn't work type this exact url into a search bar: https://www.jake4maths.com/3.2Generator.php)
A lot of these resources start at the very basics (teaching you how to plot straight lines manually) but may be useful if you want to go back to the beginning. We will use desmos for our internal so a lot of the manual work is obsolete now :)
Resources
Resources
Practice Internal Tasks
Practice Internal Tasks
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