My problem is this.(adsbygoogle = window.adsbygoogle || []).push({});

I work on a mine, trucks have a average weight that they can carry (should be approx 180 tonnes)

Every end of shift, the weightometer reading at the crusher is taken and the number of loads for each truck is stored in a database.

Trucks have weightometers but I dont trust them and I would like to calculate what the individual truck factors should be by using linear algebra or a similar method.

A truck factor is important because the loaders load using truck weightometer readings and a faulty weightometer means that the right truck factor is not applied.

The matrix equation is [a]*[tr] = [cr]

a can be a square matrix with as many days as there are trucks.

tr is the unknown to be solved which represents the weight (truck factor) for each specific truck.

cr is the row vector of the daily crusher readings taken.

This can be solved by taking the inverse of matrix [a] and multiplying with [cr]

[tr] which I calculated proved to be useless as it contains negative values and values of up to 300 tonnes. I assume it has something to do with the sensitivity of the problem.

This got me to thinking, the inverse is simply the minimum of the vectors in an unrestricted domain minimising abs([a]*[tr] - [cr]) and I know that a truck cannot conceivably weigh more than say 220 tonne and less than 120 tonne.

Are there any mathematical methods out there that can minimise abs([a]*[tr] - [cr]) where each individual value of [tr] must fall within the range specified (120-220)?

My mathematical ability and background is about 3rd year Engineering Maths.

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# Minimising a vector over a restricted range

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