Is it regression I need?

I'm trying to establish a formula to predict output based on some sample data.

We produce items of different sizes... Small, Medium, Large. Also, we use sometimes a different number of employees to produce the items.

I would like to end up with some formula such as:

1.4 x SML + 1.1 x MED + 0.6 x LRG = Predicted Output

Is it regression that I need to do this? It's been a while since I used that, so I'm not sure if it works when adding together the input variables always equals the output. I'm just looking for the relationship between them. If possible, I'd like to see how the number of employees affects it as well.

Any help is greatly appreciated!

Here's some sample data:

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I suppose the question I'm trying to ask is... "how many days would it take to produce a certain combination of sizes (ie. 1500 small and 60 large)". All the data represents an 8 hour shift.

I'm not sure how Solver might help... I'm not trying to maximize or minimize anything. I'm just trying to predict based on historical data.

Thanks!

I don't think there's enough information given to understand how things are interrelated. I can see from your sample data that total pieces=sum(small:large), but, beyond that, I can't see how you want to interrelate things. Perhaps a few questions to better understand what you are working with:

1) Is each row one day's work?

2) Assuming 1 is true, how does "number of people" fit into the model? Is there an allocation formula that needs to be applies (ie for day 1, 50% of people are assigned to small, 25% to med, and 25% to large)?

3) Are there other factors that go into how many of each item is produced?