Linear Programming - Example 1


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Linear Programming with GeoGebra - Example 1

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Problem*: 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?

Solution

 

The Problem asks how many cabinets A and B so we let these be our variables:

  • Let x=number of cabinets of type A and let y=number of cabinets of type B.
  • This is a real problem so our 1st and 2nd constraints are:  x ≥0 and y ≥0.
  • Price gives our 3rd constraint: 10x+20y ≤ 140  and
  • Floor space (footprint) gives the 4th constraint: 0.6x+0.8y ≤ 7.2
  • Finally, our objective function which we need to maximize is volume:  V=0.4x+0.6y.

Let's solve this problem using GeoGebra!  Watch the mathcast, study the interactivity below and then do it yourself.

YouTube Mathcast

 

YouTube plugin error

Note: I forgot to test the intersection point O(0,0) ...

InterActivity with GeoGebra

 

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)

*Problem adapted from: http://www.purplemath.com/modules/linprog3.htm 
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