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Linear Programming - Educator Page

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Linear Programming with GeoGebra - Educator Page

How and Why   UP

Pitfalls for Educators

Pitall 1: Problems in linear programming involving "whole things" like filing cabinets are a bit tricky to adapt.
Usually this means checking that the coordinates of the intersection point of the main constraint equations are whole numbers.

Pitall 2: You must check that the final shaded area is convex (no star points).

Luckily, we can easily check these with GeoGebra!  Try it with the interactivities in the example below!

Example with YouTube Mathcast and GeoGebra InterActivities:

Let's look again at Example 1: where the answer is numbers of filing cabinets. This means x and y can only be whole numbers.

 Example 1: We need to put file cabinets in our office. File cabinet A costs 10 Euros, has a footprint of 0.6m2, and a storage capacity of 0.4m3. File cabinet B costs 20 Euros, has a footprint of 0.8m2, and a capacity of 0.6m3. We can spend a maximum of 140 Euros and we have a maximum floor space of 7.2 m2. How many cabinets of type A and type B should we purchase to maximize our storage capacity? Our constraints were:  x ≥0 and y ≥0, 10x+20y≤140 and 0.6x+0.8y≤7.2 and our solution was the whole numbers x=8 and y=3.

Pitall: Changing the numbers in the constraints 10x+20y≤140 and 0.6x+0.8y≤7.2 ...

We must check that the area is convex and that points A, E and D are gridpoints (or only E if we are in a hurry).

 YouTube Mathcast GeoGebra InterActivity 1: Just changing the totals (2 numbers) Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now) GeoGebra InterActivity 2: Changing all the numbers Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now

Pleasures for Educators

Pleasure 1: You can always change the numbers in the objective function as desired!

Pleasure 2: You can make GeoGebra worksheets with sliders to change the parameters of the problem. Then you or your students can make up good problems and have interesting discussions about what is happening. Watch the YouTube mathcast and then DIY in the GeoGebra interactivity below.

DIY Example with YouTube Mathcast and GeoGebra InterActivity:

DIY InterActivity with GeoGebra     Directions for InterActivity

 Remember - only gridpoints in the purple-shaded area satisfy our constraints. • First practice with the interactivities in the example above. Our goal is to make these interactivities. • The numbers in the objective function do NOT matter! Only the intersection points of the constraint equations. • Quick: Make 2 sliders for the           == total cost ct from 0 to 200 increment 10 and           == total footprint fp from.from 0 to 10 increment 0.1 • In the Algebra View, double-click on line a and change x+2y=14 to 10*x+20y=ct and then on line c and change  7.2 to fp. • Now slide sliders for ct and fp until E is a gridpoint. • More changes: Make 4 more sliders for the cost of x and cost of y: ctx and cty and for the footprints of x and y: ftx and fty. • In the Algebra View, double-click on line a and change 10x to ctx*x and 20y to cty*y and then on line c and change  7.2 to fp. • Now slide all sliders until A, E and D are gridpoints.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

 Global Linear Programming in 2 Variables Brief YouTube Mathcasts and GeoGebra InterActivities Docs Worksheet and Survey for Example 3 , How&Why Directions Grade 10th and up (Systems of Linear Inequalities) Strand Algebra 2, Linear Algebra, Operations Research Standard CA 2ALG 2.0, ACT EE33-36 Keywords linear programming, constraints, inequalities, plane, objective function, algebra 2, geogebra, freeware Download Double-click on GeoGebra files to open and save, , Author LFS - contact Credits Zoran Trifunov (slider/line idea) and Dani Novak (google doc and survey) Type Freeware - Available for Offline Use - Translatable (html) Use Requires sunJava player