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so basically when you hit 901 real shipments, it becomes profitable to send 1000 - (number of real shipments) empty envelopes, at a total savings of $3 * (number of real shipments - 900).

(For number of real shipments <= 1000)



It's even less than that. The equation that describes the decision to send envelopes is:

0.9(3n + 1000 - n) < 3n

Which is the same as n > 750.


Shit I just spent an hour researching this !

Something was fishy in your inequation here is my result :

3x > 3x+(1000-x-300)

So this means that at x > 700 it is profitable to send empty enveloppes.


I think your equation is modeling an exact savings of 300 for sending 1000 pieces of mail. The discount is 10% for sending 1000 pieces.

Mine is simply comparing the cost of sending n pieces of mail at $3 each to 90% of the sum of n pieces at $3 each and 1000-n at $1 each.


Yes I assumed a 300 flat rate from the previous comment, but you're right he mentions 10% in his post.




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