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Optimizing structure for toppling

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Hi! everyone...

I'm a building a standing frame for disabled children, the structure in elemental form is shown in picture.

link to picture - https://drive.google.com/file/d/0B60...it?usp=sharing

Now, I want to optimize the structure for toppling, lets say a force, F is acting on the top most part, fig(a).
I can change dimensions but there are certain limitations like minimum length of the frame, maximum width and maximum weight of the plate. So, how do I optimize all these things keeping in condition that frame doesn't topple??

Also, can I do better optimization by changing structure as shown in fig(b), and fig(c)? if yes, how?

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