The knapsack problem with setup  (KPS)  is a challenging problem  in combinatorial optimization. This paper deals with the generalized problem of KPS called multiple-choice knapsack problem with setup (MCKS). The MCKS has several applications in industry such as the assignment of production to plants. A combination of Iterated local search with  integer  linear  programming  is  provided  and  enhanced  by  LP-relaxation  to  solve  the MCKS.  The  provided matheuristic is called LP-ILS&IP. A sensitivity analysis is provided the justify the components of the LP-ILS&IP and numerical experiments are conducted on a set of 120 benchmark  instances  to show  the competitiveness of  the LP-ILS&IP compared to the best state-of-the-art solving techniques.