This is a real-world math/logic problem and I thought that since there’s a few geeky, math-types out there who read this (okay, two, maybe three) I’d throw it out there to see if you can help.
We have Board meetings twice per month. We send out the meeting materials on CD-RW to approximately 25 people each meeting.
Because the return rate is not 100%, one of the assistants asked if it would be more cost effective to buy CD-Rs instead.
CD-RWs: $11.29 per 25-pack (about 45 cents per CD)
CD-Rs: $19.86 per 100-pack (about 20 cents per CD)
The return rate is somewhere between 50-66.66% each meeting, but we can reuse the CD-RWs a dozen times (in theory).
I’m going to try and figure it out on my own, but I am not confident that I will return the appropriate result.
6 Comments
March 6, 2009 at 12:32 pm
It appears that you’re spending about $5.50 per meeting on CD-RWs since you have to replace the ones that don’t get returned. The CD-R’s, however, cost right around $5/meeting. So it’s only about a 50 cent per meeting savings, so might not be worth it.
(This doesn’t take into account replacing the RWs after a dozen uses or anything, though).
March 6, 2009 at 12:40 pm
Yeah, it turned out to be an easier problem than I thought. Since those #s are the higher end #s, the difference per meeting is probably less. I don’t think the uses per CD really matter unless we wanted to look at the cost over several years.
March 6, 2009 at 12:49 pm
Using the lower return rate (50%) and decaying the CD-RWs from 100 (45 dollar investment) using 25 CDs per meeting you get…
100 -> 87 (75 new + 12 used) -> 74 -> 61 -> 48 -> 35 -> 22
Which means you get 6 meetings out of you $45 investment (the 7th you are 3 CD short)
With CD-Rs, you could get about 225 CDs for the same $45 investment. Decay for these is much simpler…
225 -> 200 -> 175 -> 150 -> 125 -> 100 -> 75 -> 50 -> 25
So you get 9 meetings for the same investment, making CD-R’s the better deal.
If your return rate is closer to the 67% mark, then the CD-RW’s are a slightly better deal (just over 9 meetings for $45) …
100 -> 91 -> 82 -> 73 -> 64 -> 55 -> 46 -> 37 -> 28 -> 20
March 6, 2009 at 2:47 pm
Total: 7 * $19.86 = $139.02 for CD-R @ 0 returned/meeting
Total: 14 * $11.29 = $158.06 for CD-RW @ 12 returned/meeting
Total 10 * 11.29 = $112.90 for CD-RW @ 16 returned/meeting
March 6, 2009 at 2:59 pm
If you continued calculating values over years, it gets a tiny bit trickier, because of the “only 12 reuses” rule. But for one yr this doesn’t affect anything.
March 6, 2009 at 3:56 pm
Another thing about reuse… it could get even more complex if you take into account that you might get different CDs returned each time (including already-reused CDs), thus varying the rate of reuse you could take advantage of.
Just fine everyone a quarter if he doesn’t return a CD.
I think I’ve overanalyzed this enough. On to the weekend!