> Do I need to call glp_delete_prob() after each LP subproblem?
> 

Yes, if you wish to free the memory allocated to corresponding
problem objects.

glp_create_prob is a constructor, and glp_delete_prob is a destructor.
In C it is impossible to automatically call destructors to delete local
objects on exit from the block (as well as constructors on entry to a
block), and since glpk has no garbage collection, you need to call 
destructors explicitly in order to free all resources allocated to
the objects that are no longer needed/referenced.


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