For each customer that calls into ABC credit card billing service call center, at the end of the phone conversation, the call center representative will offer each customer ONE of the following two products, a personal loan or a payment protection plan.

Two logistic regression models are used to predict the probability of each customer accepting each of the two offers based on their outstanding balance and credit score.

Probability of accepting a personal loan offer =

exp(-5.8753+0.0016*outstanding balance)/(1+exp(-5.8753+0.0016*outstanding balance))

Probability of accepting a payment protection plan =

exp(-0.2526-0.0033*credit score)/(1+exp(-0.2526-0.0033*credit score))

The annual profit for a personal loan, if accepted, can be estimated with the following linear regression model:

Annual profit of a personal loan =

45.2568 + 0.1245*outstanding balance - 0.0122*credit score,

and the annual profit for each payment protection plan, if accepted, is at the fixed value of $120.

Which one of the two products should be offered to James, who has the outstanding balance of 1600 dollars and credit score of 660?

(Hint: use the notion of expected value to incorporate profit of an offer and probability of accepting an offer. )