Consider our telco churn example from class. we would like to target some subset of our customers with a brand-new special offer prior to the expiration of their contracts, in order to minimize our losses due to churn. the special offer has a fixed cost of c irrespective of whether the customer accepts it. as we mentioned in class, in a real business application you want to design your solution carefully and specific to the application. you can assume that the value of a particular customer group, if she were to stay, can be estimated directly using this particular customer’s past value and knowledge of the business going forward and the incentive. we would like to see whether our investment customers tend to cluster in understandable groups.