An interesting application of Optimization;

My Math teacher tells me that there can be _no_ uninteresting numbers. If there _were_ a set of all x's such that each and every x is an element of the set of uninteresting numbers, there would be a smallest uninteresting number, and that would be interesting! I tried to theorize that there might be exactly one, but this theory quickly fell to the observation that, if this were the circumstance, it would be Unique, and interesting for THAT reason :-)

I can understand that individual numbers are not intrinsically fascinating, so I use the word "interesting," to characterize my application of recently discussed Optimization, in context of relativism.

A vault is useful for retaining valuables, but costly. My application of optimization attempts to answer the question: Is a $7,548 Safe a good investment to secure my $100,000 Bearer Bond?

I will fictitiously attribute the Brand to be "Kalashnikov and Sikorsky."

Bearer Bonds have been tested against oxidation, and they are perishable at temperatures in excess of 317 degrees F.

K&S model AR15 keeps the internal temperature below 300 degrees F for 72 minutes in a 1200 degree F fire, before succumbing.
Against a drill bit, K&S-AR15 takes 6 hrs and 37 minutes for the Wolf 7000, the best drill in the world to date.
The combination is 3 numbers, 0 to 80. While all combinations MUST take the form that the second number is HIGHER than the first, with the third lower than them both, there is STILL a satisfyingly high number of them. I evaluate that a lifetime has approx 2.5 B_illion seconds in it, so even at one a second without a pause for the niceties of toiletry, a human couldn't foil the mechanism by brute mathematical force. In fact, most criminals have a career shorter than 67-21 yrs (46,) and this is only 1.45 B_illion seconds. More to my contentment, there are only 57.6 thousand seconds from the end of an 8 hr shift to the beginning of the next. A drop in the bucket of available combinations for my K&S-AR15.
Since it is not electronic, loss of electric power cannot compromise it, nor can Harpie Sharpie, known safe-cracker devise an electronic key to by-pass the human factor. On balance, I cannot _CHANGE_ the combination easily; the expense involved is more than a $100,000 Bearer Bond is worth. I will have to limit key distribution in some way.
Harpie Sharpie has been known to foil a safe by creative application of sand-paper to his fingers. This requires physical access, and 3 hrs 42 minutes. I salve my fears by reminding myself that he is prone to be stealing diamonds in S. Africa to finance his favorite pastime of attempting to steal Rembrandt's "Night Watch." The concierge at the Johannesburg Hilton tells the Louvre every time he scores, and they move the painting to a new museum every two weeks until Harpie runs out of the ready green, and goes back to diamonds again. Other than that, Harpie is the best, so others will be less likely to succeed. I do not neglect to make it hard to access the restroom from the Vault after hours, and caffeinated beverages are nearby, (for a price,) while Adam's Ale is metered at a water fountain traditionally next to the lavatory.
I have read books on Antique books, and I reckon that my Bearer Bond will be a collectors' item from year 58 to year 300 or so, after which it will be too tattered to matter. My K&S-AR15 vault should be fine for that long at least... it doesn't rain much inside the Library, and the books are humidity controlled as well. I make a note to keep up with Drill bit R&D, in case they improve on the Wolf 7000.

I am now ready to attempt my time-value-retained is as to cost-per-dollar-day gestimation. (I am by no means rigorous as to the units of measure or desirable ratio.)

Cost of a safety deposit box for 300 years = $65 * 300 = $19,500.
Cost of K&S AR15 = $7548, amortized over 30 years::16,734.20 @ $46.47 per month.
Library Insurance against Fire's hotter than 1200 degrees for 72 minutes = $741.37 per annum. Payout = Library replacement cost, plus authentic $100,000 collectors' item Bearer Bond, as purchasable on E-Bay.
Insurance against Bad Employees with Loyd's of London - $71.49 per quarter. Payout = (Current cost of changing tumblers) OR (new comparable Vault,) whichever is less.

I will now compute my personal optimization table.

Factors:

1. Time to Bearer Bond Perishing in Vault - Maximize.
2. Temperature within K&S AR15 - Minimize.
3. Time to drill with Wolf 7000 or other best available drill - Maximize.
4. # of Combinations = don't go overboard.
5. Price to change combination tumblers - Minimize.
6. Time it takes to change tumblers b/c of bad employee - Minimize
7. Obligatory Security Guard to keep Harpie Sharpie on his best behavior? - Minimize (again, don't go overboard.)

I am happy with this list. If I felt the need to make the Combination electronic, I would HAVE to figure cost per time of electric usage. If I centralize monitoring so the security guard doesn't have to walk around, I have to figure cost of alarms (power bill included,) phone bills to central location, and my house, etc.

Although I appear to have be specific enough to be rigorous (specific enough to be humorous for CERTAIN,) we lack other numbers against which we may compare and contrast Vault values. Like an amortization table, the computations to "fiddle," might be arduous, but it illustrates that if you are prepared to be creative, you can find purchase on some pretty hard to quantify problems this way. I hope it is helpful.