🚀 go-pugleaf

richb@nando.net writes:

> 
> You have 7 fertilizers:
> 	
> NAME		PRICE/TON
> ---------		-------------------
> Filler (0-0-0)	30
> 21-0-0		98
> 0-0-60		108
> 0-46-0		136
> 0-0-22		148
> 46-0-0		200
> 18-46-0		207
...
> Problem:
> 
> Find the least cost (LCM) for a blend of 10-20-20.
> Please, if you choose to accept this mission, post the algorithm on
> this newsgroup and PLEASE e-mail me at richb@nando.net.

Others have mentioned linear programming.  I just tried to solve it
logically:

There are two K-only mixes, and no other mixes provide K.  The better
buy is K=60.  So we need 1/3 0-0-60, and 2/3 15-30-0.

Only one mix gives both N and P.  Subtracting the P-only price, the
  price for N in it is cheaper than N-only mix.
Only one mix gives P-only.
46-0-0 is the best-buy for N-only.

To make using 18-46-0, we need
  30/46 of 18-46-0
  plus 
  16/46 of 9.375-0-0

We can make the 9.337-0-0 from .2038 of 46-0-0 and .7962 of filler

So if I did it right, it's:

(30/46) * 207 +
(16/46) * (.2038 * 200 + .7962 * 30)
= 135 + 8.3082 = 143.31 Least cost

Note that followups are redirected to comp.programming.contests, which,
though not in the original list of newsgroups, struck me as most appropriate.

-- 
-------- Roy Johnson ---- rjohnson@shell.com ---- Speaking for myself --------
"When the only tool you have is Perl, the whole | "Hooray for snakes!"
 world begins to look like your oyster." -- Me  |  -- The Simpsons (29 Apr 93)
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