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I have a list of costs that a vendor charges for various products and know the components of each product. There is substantial overlap in components of the products - for example product A costs 100 and is comprised of 3 bolts, 5 gears and 1 enclosure and product B costs 150 and is comprised of 1 bolt, no gears and 2 enclosures, etc. How can I make a best estimate of the vendor's internal costs by component?

I tried making a spreadsheet that computes the least square sum given guessed components costs and fiddled with component costs. I found that without too much effort I could minimize the sum of squares. However I found that starting with a new set of starting values for component costs I often arrived at a different least sum. In other words it did not seem to be "stable".

How can I make the search stable? And how can I avoid fiddling with the component values manually?

I searched questions here and followed various links from Wikipedia to no avail.

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If you have three products, you can use matrices and Cramer’s rule or any other method to solve the simultaneous equations represented. Below is the setup for the two examples you provided for Bolt, Gear, and Enclosure. (The dots are just for spacing.) You will need three products and the base determinant must be non-zero for there to be a solution at all. Also note that this approach is naive in that it assumes that the cost of components is the entire cost of the product.

B....G....E

3....5....1 = 100

1....0....2 = 150

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  • $\begingroup$ I think that will not apply because I am assuming that the vendor is not pricing perfectly rationally. I need a "best fit" approach. $\endgroup$
    – Jim Lewis
    Apr 4, 2018 at 9:16

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