Formulation Of The Problem

Then,
(1) I=∫a.x.dt + ∫[W(t) – x].θ [W(t) – x]. (a+b) dt,
where θ[W(t) – x] is the well-known step function
Or,
12 12
(2) I=Σ (a/12).x + Σ [(a+b)/12].[Wi – x]. θ[Wi – x].
i=1 i=1
where Wi=level of working capital finance for the ‘i’th month