# Optimum pack size purchases: part 3

Suppose I need quantity Q grams of honey, and I can buy packs of honey in either 340g or 454g pack sizes. These packs cost 1.79 and 2.19 respectively (cost per kilo is therefore 5.26 and 4.82 respectively)

I buy m packs of 340g and n packs of 454g

Question: express m & n in terms of Q in order to minimise cost for any given Q.

I believe this is a solution: https://www.experts-exchange.com/questions/29063883/Optimum-pack-size-purchases-follow-up-to-minimum-cost-solution.html

But this maybe overbaking it (the least common multiple of 340 and 454 is 77180)

Wandering if I'm missing a shortcut somewhere.

Thanks
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PrincipalCommented:
Well, I'd like to make sure the logic is clear, so:

1) Note that 454<2*340 so one would purchase as many of the larger packs as possible and then only one additional pack is needed of one size or the other.

2) Plan to purchase as many of the lower-cost packs as possible:
That quantity is n'=ROUNDDOWN(Q/454)

3) Plan to purchase the remaining quantity P=Q-n'*454.  If P<=340 buy one of the smaller packs.  ELSE buy one of the larger packs.
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Author Commented:
Thanks Fred, that's exactly right. I believe in this case that summarises the solution completely.

I will post a follow-up working towards more complicated examples.
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