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Additional Maths Help

I am doing GCSE FSMQ this year and I am struggling with a section on Linear Programming. This is to do with the objective function - I am told that it is "usually near a vertex" of the feasible region, though it does not specify which vertex. The book simply picks one vertex out of three and works with that one. So, my question is: is there a method for determining which vertex has the best solution?
Original post by Hariex
I am doing GCSE FSMQ this year and I am struggling with a section on Linear Programming. This is to do with the objective function - I am told that it is "usually near a vertex" of the feasible region, though it does not specify which vertex. The book simply picks one vertex out of three and works with that one. So, my question is: is there a method for determining which vertex has the best solution?


You can work out the value at each vertex

However - if you are looking for the highest value you want a vertex as far from the origin as possible
Reply 2
Original post by TenOfThem
You can work out the value at each vertex

However - if you are looking for the highest value you want a vertex as far from the origin as possible


Thanks for your help.

Why is the highest value the furthest from the origin? Is it because the x and y values will definitely be large than the other vertices?
Original post by Hariex
Thanks for your help.

Why is the highest value the furthest from the origin? Is it because the x and y values will definitely be large than the other vertices?


yes
Sometimes there is a function to maximise and you consider which of the vertices of the region gives the highest value.
Original post by Muttley79
Sometimes there is a function to maximise and you consider which of the vertices of the region gives the highest value.


I would have thought that all questions had a function to maximise (or minimise)
Original post by TenOfThem
I would have thought that all questions had a function to maximise (or minimise)


I have seen questions where you just have to find the solution space.
Original post by Muttley79
I have seen questions where you just have to find the solution space.


Oh yes, I just meant - given he was talking objective function :smile:

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