Rob Richman, president of AmeriBank is bothered about the state of his bank. AmeriBank, a medium-sized bank with branches throughout the United States, is headed for dire economic straits. The bank is simply losing customers to nonbank and foreign bank competitors. Many American banks have been suffering significant losses because of increasing competition from nonbank and foreign bank competitors offering services typically in the domain of American banks. Rob has one strategy for distinguishing AmeriBank from its competitors is to improve services that nonbank and foreign bank competitors do not readily provide transaction services. Internet allows this convenient transaction method. Over the Internet, customers are able to perform transactions on their desktop computers either at home or at work. Rob needs to understand the market for Web banking and the services AmeriBank should provide over the Internet. Like balance inquiries, transactions, limitations, recapture a portion of the investment market by continuously running stock prices and allowing customers to make stock transactions over the Internet for a minimal fee. Rob has decided to outsource the survey project to a professional survey company. He has opened the project up for bidding by several survey companies and will award the project to the company which is willing to perform the survey for the least cost. Sophisticated Surveys is one of three survey companies competing for the project. Rob provided each survey company with a list of survey requirements to ensure that AmeriBank receives the needed information for planning the Web banking project.
He tries to acquire information about the age groups of account holders, their internet usage ability, income levels, and investment behavior. AmeriBank wants to interview 2,000 customers with at least 20 percent from the first age group, at least 27.5 percent from the second age group, at least 15 percent from the third age group, and at least 15 percent from the fourth age group. Rob wants to ensure that the survey includes a mix of customers who know the Internet well and those that have less exposure to the Internet. To ensure that AmeriBank obtains the correct mix, he wants to interview at least 15 percent of customers from the Silicon Valley where Internet use is high, at least 35 percent of customers from big cities where Internet use is medium, and at least 20 percent of customers from small towns where Internet use is low. Sophisticated Surveys has performed an initial analysis of these survey requirements to determine the cost of surveying different populations. The costs per person surveyed are listed in the following table: Sophisticated Surveys explores the forthcoming options cumulatively.
Region 18 to 25 26 to 40 41 to 50 51 and over
Silicon Valley $4.75 $6.50 $6.50 $5.00
Big cities $5.25 $5.75 $6.25 $6.25
Small towns $6.50 $7.50 $7.50 $7.25
Sophisticated Surveys explores the following options cumulatively.
(a) Formulate a linear programming model to minimize costs while meeting all survey constraints imposed by AmeriBank.
(b) If the profit margin for Sophisticated Surveys is 15 percent of cost, what bid will it submit?
(c) After submitting its bid, Sophisticated Surveys is informed that it has the lowest cost but that AmeriBank does not like the solution. Specifically, Rob feels that the selected survey population is not representative enough of the banking customer population. Rob wants at least 50 people of each age group surveyed in each region. What is the new bid made by Sophisticated Surveys?