## Mortgage Company obtains business from direct marketing letters signed by a fict

Mortgage Company obtains business from direct marketing letters signed by a fictitious loan officer named Jackson Smith. The percentages of interested responses from Jackson Smith letters are triangular with parameters 1%, 1.2%, and 2%. Of those responding, the percentage of respondents that actually close on a loan is also triangular with parameters 10%, 15%, and 18%. The average loan fee for a Jackson Smith loan is \$3,500 with a standard deviation of \$650. Other loan requests are  obtained from two other sources: referrals and repeat customers, and unsolicited customers obtained from other advertising (billboard ads, Google searches, and so on). Fees for referrals and repeat customers average \$2,600 with a standard deviation of \$500 (these are less in order to provide an incentive for future business), and unsolicited customers’ loan fees are the same as Jackson Smith loans. The company has 15 loan officers. Each loan officer will close an average of one loan per month from referrals and repeat customers, and about one loan every four months from unsolicited customers (use judgment to define a reasonable uniform distribution around these averages). The company is moving to a new office and will double in size. This requires them to cover additional overhead expenses. The general manager wants to be 90% certain that the office will close at least \$600,000 in total loan fees each month from all sources. The principal question is how many Jackson Smith letters should be sent each month to ensure this. Develop a simulation model to help identify the best decision.