Wikipedia:Reference desk/Archives/Mathematics/2022 July 22

= July 22 =

Cost per piece
This can't be as tricky as I'm making it. We're trying to develop costs per piece at work. We know that, in a given week, the total cost to perform the work comes to, say, $100,000 and we know that we picked 160,000 pieces. So, as a whole our cost per piece is easy - it's $100,000/160,000 = $0.63. So far so good! We have ten customers and we know exactly how many pieces each one got: Alice bought 25,000, Bob got 23,000, etc. We know the average cost per piece anyway, but we could multiply out the ratio of pieces to get the total wages spent to pick each customer if we wanted. Picking for Alice cost $100,000 * (25,000/160,000) = $15,625. Again, all good! But it turns out that the orders Doug and Fiona place are a lot easier to pick. In the time it would normally take us to pick 100 pieces for another customer, we can pick 140 pieces for those two. How can we figure out the costs per piece that take advantage of that information? I can't just gimmick those two numbers by 40%; if I do that, the totals would no longer line up - I somehow need to tweak all the values to incorporate this info. Whatever Doug and Fiona's new values are, we know that Alice's can't be $15,625 - it must be a higher share. I feel like my nose is getting too close to this and the formula isn't as hard as I think, but I'm stuck. Any thoughts? 70.24.163.21 (talk) 02:29, 22 July 2022 (UTC)
 * At the start, don't total up the number of pieces, total up the amount of time. If Alice's pieces take 1 second each, you spent 25000 seconds on her.  If Bob's take .7 seconds each, you spent 23000*.7 = 16,100 seconds on him.  Then divide the total cost by the total time to get the cost per time, and multiply each person's time by that to get their share of the cost.--2406:E003:812:5001:B804:16BB:D688:9729 (talk) 04:45, 22 July 2022 (UTC)
 * Thank you! I knew I was over-thinking things... 70.24.163.21 (talk) 17:53, 22 July 2022 (UTC)