13 A salesperson for Fuller Brush has three options: quit, put forth a low-effort level, or put forth a high-effort level.

Suppose for simplicity that each salesperson will either sell

$0, $5,000, or $50,000 worth of brushes. The probability of each sales amount depends on the effort level in the manner described in Table 8.

If the salesperson is paid $w, then he or she earns a benefit w1/2. Low effort costs the salesperson 0 benefit units, while high effort costs 50 benefit units. If the salesperson were to quit Fuller and work elsewhere, then he or she could earn a benefit of 20. Fuller wants all salespeople to put forth a high-effort level. The question is how to minimize the cost of doing it. The company cannot observe the level of effort put forth by a salesperson, but they can observe the size of his or her sale. Thus, the wage is completely determined by the size of the sale. Fuller must then determine w0  wage paid for $0 in sale, w5000  wage paid for $5,000 in sales, and w50,000  wage paid for $50,000 in sales. These wages must be set so that the salespeople value the expected benefit from high effort more than quitting and more than low effort. Formulate (and solve on LINGO) an NLP that can be used to ensure that all salespeople put forth high effort. This problem is an example of agency theory.