Fun maths question, correlation?

[Ronan]

Say i m in the cinema and there are 4 seats. say the closest seat is the
best view which is 4 meters away. say the further the distance away the
worse the viewing quality. eg [5,6,4,9] are the distances of seats away from screen.
Now let's say people sitting in front of you also effects viewing quality.
eg a tall person.

So for the same corresponding seats the level of obstruction (on a scale of 1-10, 1 being small obstruction and 10 being a big obstruction) of the view from people sitting in front of you is now [7,8,9,5]. which seat is the optimal viewing position?

I ask this because of a problem that's hard to explain but is similar to
the analogy i have explained. Maybe I am asking an impossible question but
i m trying to correlate the smallest value of one array with the optimal(smallest)
value of the other array. Is this simply solved by multipling each corresponding
value and then getting the smallest. eg

5*7 = 35
6*8 = 48
4*9 = 36
9*5 = 45

a distance of 5 meters with viewing quality of 7 is the optimal view?
I m guessing there is some kind of mathematical function out there for a question
like this.

 

[Ronan]

So best obstruction is at worst seat (9m and 5) and best distance is at worst obstruction (4m and 9)
Which is better/more optimal?

 

[jbriggs444]

Mathematics does not prescribe a particular way to optimize for a combination of multiple valuation functions. You have to decide for yourself how "good" or "bad" particular combinations of screen distance and view obstruction are.

There is, however, the concept of "pareto efficiency". http://en.wikipedia.org/wiki/Pareto_efficiency

 

[bahamagreen]

Ronan,

Looks like the thing you are trying to do is very similar to the calculations of risk assessment where you have a list of hazards and want to best use your resources to mitigate the most loss for the least resource consumption. Each hazard is evaluated for how serious it would be if it happened (potential loss), and for the probability that it might happen. Multiplying the potential loss by the chance of it happening gives values called risks used to rank the hazards against some threshold chosen to distinguish acceptable hazards from hazards to be subjected to mitigating actions (actions which reduce either or both of their potential loss or probability factors) to get their risk values under the threshold.

Do a search on risk assessment and see if that numerical methodology looks like what you are thinking about. :)