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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 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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