Can you fit it as a nonlinear model of the form y = exp(b1)*x1 + exp(b2)*x2 + etc in situations where all the parameters have to be positive? Similarly, put a minus sign in front of any exp(bi) where the parameter has to be negative, given that any exponential term must necessarily be positive.

Also - and this may be overkill for what you're trying to do - but take a look at the online Help | Sample Data index, expand the "Nonlinear Modeling" section and load the "Algae Mitscherlich" data set. If you then click on the "Full nonlinear model" red triangle on the left of the data table and select "Run script", you'll be presented with a control panel which provides among other things the means to impose lower and upper limits on any or all your parameters. I appreciate that your model is essentially linear, but I can't see any reason why the nonlinear platform can't be used to solve the problem instead - and the ability to impose explicit constraints on the parameters looks potentially very useful in this context.

The nonlinear formulae themselves can be found among the properties of the "Mitscherlich", "equal alphas" and "equal betas" columns of the data table: to see and/or edit them, right-click on one of the column headers, select "Column Info" and then "Edit Formula". The nonlinear platform can be loaded for any data set of your own by selecting Analyze | Modeling | Nonlinear from the main menu: once the control panel has loaded, click on the "Help" button for assistance on building and fitting nonlinear models.

Does that help at all? I admit I'm not familiar with this platform myself, and I'd be reaching for the manual myself to work out how to use it, but at first sight it looks as though it's more than capable of doing what you require if you can work through the relevant documentation.