A bit of background first-- I started a position palletizing in a fruit factory. Basically what we do is take dried fruit and package it.

As palletizer I am responsible for recording the total # of cases(total cases or TCS), the weight of the total cases (actual or A), the weight of the fruit that was used (total raw pounds or TRP), the weight of the fruit recovered from all nooks and crannies of the machinery at the end of the day (Salvage or S), and the percentage of fruit lost (%).

For example:

Today we ran 15 pallets of mangos. Each pallet contains 40 boxes that weigh 37.5 lbs. each.

They were packaged into 28 oz. bags, 12 bags per case, 24 cases per pallet.

We end with 43 pallets and 650 lbs. of salvage.

After gathering all of this information, it is then time to calculate the loss %

What we've gathered:

TCS: 24 cases x 43 pallets = 1,032 cases
A: [28 oz. x 12 bags = 336 oz. OR 21 lbs] 1,032 cases x 21 lbs = 21,672 lbs.
TRP: [40 boxes x 37.5 lbs = 1,500] 1,500 lbs x 15 pallets = 22,500 lbs
S: 650 lbs

Now to find the loss percentage we subtract the S from the TRP to get TwoS (Total without Salvage), subtract A from TwoS to get the loss (L) in pounds, divide by TwoS, and multiply by 100 to get the final percentage.

So

22,500 - 650 = 21,850
21,850 - 21,672 = 178
178 ÷ 21,850 = 0.0081464351
× 100 = 0.814%

So for me to learn this with a high school math level was well, fairly easy but it took a day or two.

But today I had a rough time, and this is where I need help.

To be brief, today we ran through 3.25 pallets of apricots (80 cases @ 28 lbs.), we packaged the fruit into 6 oz bags with 12 bags per case and 160 cases per pallet. 201 cases are shipped to vendor A, while the rest are shipped to vendor B. Due to the small weight of the bags, its difficult for the machine to produce accurate results, resulting in a loss due to overweight bags. Because of this, my lead gives me direction to manipulate the numbers so the loss percentages for both orders are in the same ballpark. Anything under 3% is considered acceptable (although sometimes there's nothing that can be done about a high percentage).

So what this means is that in reality 42 boxes were used to produce the 201 cases, but due to the fact its a small amount with overweight bags the % is around 14% (completely unacceptable). We have to bring that down to 3% by taking or removing TRP from A to B. We also have to pretend there was at least a little salvage in A's order which means pretending more TRP was used (The S from A will then be added into B's TRP).

What I'm now wondering is what kind of math can be used to calculate this so I can study on my own. While this may be simple to most mathematicians, it is highly stressful for me to calculate due to the fact it's one of many tasks I am required to complete. That said I'm looking for the fastest possible process to calculate this so that I dont have to think so much and I can let the process do the work.

Anyway I hope I explained this clearly. If any clarification is needed please ask and I will reply promptly. Thank you anyone who reads and shares their thoughts.