A dual-weighted residual approach for goal-oriented adaptive finite elements for a classof optimal control problems for elliptic variational inequalities is studied. Thedevelopment is based on the concept of C-stationarity. The overall error representationdepends on primal residuals weighted by approximate dual quantities and vice versaas well as various complementarity mismatch errors. Also, a prioribounds for C-stationary points and associated multipliers are derived. Details onthe numerical realization of the adaptive concept are provided and a report on numericaltests including the critical cases of biactivity are presented.