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Problem*: We need to put file cabinets in our office. File cabinet A costs 10 Euros, has a footprint of 0.6m^{2}, and a storage capacity of 0.4m^{3}. File cabinet B costs 20 Euros, has a footprint of 0.8m^{2}, and a capacity of 0.6m^{3}. We can spend a maximum of 140 Euros and we have a maximum floor space of 7.2 m^{2}. 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 andy ≥0.

Price gives our 3rd constraint: 10x+20y ≤ 140 and

Floor space (footprint) gives the4th 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

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

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