Does this even make sense?

Am told to do a multiple regression analysis. The response variable and the explanatory variables add up and should give a percent of the total product. Example:

Milk = water + fat + protein + e ~= 96% (all are in terms of percentages, 96% is the average total from the dataset)

where e is the error such that e~NID(o,sigma)

The regression I was asked to do is

protein = β + water*x1 + fat*x2 + e

We want this so we can calculate protein without having to measure it (data is from some test samples)

This to me makes absolutely no sense...Since the equation is just

protein = -water-fat-e +100

so the coefficients should be negative 1 and beta = 100???

Would it be more appropriate to do a hypothesis test as such:

Protein + Water + Fat ~= 96% of total milk weight (the total average is the average from data)

Hypothesis test:

H0 := (Water + Fat) - Protein = 45.1 (average difference obtained from data)

H1 := (Water + Fat) - Protein != 45.1

Not sure what analysis would be best and any help would be most appreciated. Thanks!