Optimisation principle
I think it would be better talking about V1/VR and V2/VS ratio for takeoff optimisation.
Depending on restriction(s). You may have a triple limitation like a second segment, TOD n-1, brake energy limitation and have as a result 2 V1/VR ratios.
One being a min. V1/VR and one being a max. V1/VR ratio. It is up to the operator to choose one.
Companies will use a performance provider (if not inhouse) for takeoff optimisation data.
This BFL is very theoritical and talks only about a specific distance, while operators are more interested in MTOW for a specific runway and conditions of the day.
The optimisation objective is to obtain the highest possible performance limited takeoff weight, while fulfilling all airworthiness requirements.
There are fixed and free parameters. Free parameters are for example, takeoff configuration, air conditioning, V1, V2.
By changing ratios V1/VR and V2/VS, operators will get the MTOW according to a specific runway, conditions of the day and aircraft configuration.
The V1/VR ratio as a minimum and is given by the aircraft manufacturer. The max. being 1 (regulatory).
Where did you get this definition 'V1 not less than 1.05 VMCG'???.
Rgds.