A systems BPS is the process of bringing its ideality and value into balance 

BPS ↔ I + V

A systems ideality is when its efficiency exceeds its problems and any harms, so an ideal system delivers the highest efficiency with no problems or harms

I  ↔ E > PH

An efficient system delivers actual output equal to or in excess of is its required output, so the most efficient system will deliver actual output at or higher than its required output

E ↔ A > R

Apply the fraction rule to simplify the formula for system Ideality, a systems ideality is when its actual output equals or exceeds its required output and any harms or problems of reaching its required output

I  ↔ A > RPH

A system is valuable when its benefits exceed the cost of the benefits, so the highest value system delivers the highest benefit with the lowest costs

V ↔ B > C

Substituting in all the definitions, a systems best result is when its efficiency exceeds required output and any problems or harms of its output plus its benefits compared to its costs 

BPS ↔ ( ( A > RPH ) + ( B > C) )

The second and third solution tests focus on identifying the delta necessary to bring ideality and value into balance.