Adding limits to regression coefficients For my problem, I have data that contains daily observations of the total time and the volumes of task A completed, task B completed, C, D.. and I am looking to estimate the time it takes to solve task A, B, C, D etc. 
[total time] = [task A time]*[volumes A] + [task B time][volumes B] + [task C time][volumes C] + ..  
Where [total time] and all [volumes _].. Are known.
Since I have tried multiple regression on this with total time as the [total time] and volumes as the independent variable but have been getting a values that are too high or too low for the coefficients (i.e. [task _ time]. 
I know roughly the upper and lower range for the time for each task e.g. 200 < [task A time] < 400. Is regression the best way to approach this problem and is there a way to factor these limits on the coefficients in the regression?

 A: Not entirely clear what you are asking. However, constraints for parameters are routine but only for certain regression methods. Also, the availability of routines that include constraints varies somewhat between platforms. For example, in Mathematica, constrained optimization can be applied for a number of regression methods including Nelder-Mead, and differential evolution. R-language, has for example, a constrained optimization algorithm. IBM's SPSS GENLIN MIXED has constrained optimization for the Newton-Raphson method using Active SET Method (ASM). 
The practical information you require is to do a search for whatever platform you are using the search term constrained optimization.
A: I remember using a levenberg-marquardt algorithm in R, using the minpack.lm package, which was extremely easy to constrain coefficients.  Although I observed some coefficients seemed to rush towards my set bounds!
This was the best I could research given box constrained regression, usually refers to set bounds of the minimum in the error surface. I think.
