Activity based formular for implementning library budget cuts

This equation is the mathematical representation of an activity based model that calculates an adjusted library budget taking as input the actual consumption / cost of library resources for a given set of subject areas, given a desired resulting reduction of the library budget in total. In the equation, "b" is the budget vector for a particular subject area, index "a". The -budget vector has 3 elements: Printed and individual e-books, print journals, and electronic resources. Annual index is "i". The cost vector is "f" for each of the subject areas "a", and contains the cost for the same 3 elements as the budget vector. Activity indicators are M and depend on subject area "a" and index year "i". The activity is weighted by the free parameter epsilon (also a vector with 3 elements). M could e.g. be student and staff volume, research production or other variable with an annual variation. There can be any number of M's to be summed and weighted by epsilon.