Consider a different version of the Traveling Salesman Problem in which the salesman collects a prize wk in every city k that he visits and pays a penalty c to every city that he fails to visit. Suppose that the cost of traveling from city i to city j is tij and there is a lower bound W on the amount of prize to be collected. Formulate the problem of finding a tour that minimizes the sum of travel costs and penalties of the salesman.