5.6 A firm that sells software services has been piloting a new product and has records of 500 customers who have either bought the services or decided not to. The target value is the estimated profit from each sale (excluding sales costs). The global mean is $2128. However, the cost of the sales effort is not cheap-the company figures it comes to $2500 for each of the 500 customers (whether or not they buy). The firm developed a predictive model to identify the top spenders in the future. The lift and decile charts are shown in Figure 5.17. Lift chart (validation dataset) 500,000 400,000 Cumulative profit 300,000 when sorted Cummulative using predicted 200,000 values Cumulative profit 100,000 using average 0 0 100 200 300 # Cases Decile-wise lift chart (validation dataset) 3 2.5 Decile mean / Global meam 1.5 0.5 2 3 5 6 7 B 10 Deciles FIGURE 5.17 LIFT AND DECILE-WISE LIFT CHARTS FOR SOFTWARE SERVICES PRODUCT PROFITa. If the company begins working with a new set of 1000 leads to sell the same services, similar to the 500 in the pilot study, without any use of predictive modeling to target sales efforts, what is the estimated profit? b. If the firm wants the average profit on each sale to at least double the sales effort cost, and applies an appropriate cutoff with this predictive model to a new set of 1000 leads, how far down the new list of 1000 should it proceed (how many deciles)? c. Still considering the new list of 1000 leads, if the company applies this predictive model with a lower cutoff of $2500, how far should it proceed down the ranked leads, in terms of deciles? d. Why use this two-stage process for predicting profit - why not simply develop a model for predicting profit for the 1000 new leads