Few companies take the time to estimate the value of a good customer (and often spend little effort to keep one). Suppose that a customer at a restaurant spends, on average, R per visit and comes F times each year (for example, if a customer purchases once every two years, then F = 1/2 = 0.5). The restaurant realizes a gross profit margin of M (expressed as a fraction) on the average bill for food and drinks. In addition, the fraction of customers defecting (not returning) each year is D. 

a. Develop a mathematical model to compute the gross profit during a customer’s lifetime in doing business with the restaurant (this is often called the economic value of a customer). 

b. If the average purchase per visit is $50, the gross profit margin is 0.4 (that is, 40%), customers visit an average of six times each year, and 30% of customers defect each year, what is the economic value of the customer?