Atlantic Management Systems is a consulting firm that specializes in developing computerized decision support systems for computer manufacturing companies. The firm currently has offices in Chicago, Charlotte, Pittsburgh, and Houston. It is considering opening new offices in one or more cities- including Atlanta, Boston, Washington, DC, St. Louis, Miami, Denver, and Detroit-and it has $14 million available for this purpose. Because of the highly specialized nature of its high-tech consulting work, the firm must necessarily staff any new offices with a minimum number of its employees from its existing offices. However, it has a limited number of employees available to transfer to any new offices. In addition, the cost of transferring employees depends on the city they are leaving and the city to which they might move. Following are the costs for opening a new office in each of the prospective cities and the start-up staffing needs at each office: Prospective Office Setup Cost Staffing Needs ($1,000,000s) (employees) 1. Atlanta $1.7 9 2. Boston 3.6 14 3. Denver 21 8 4. Detroit 25 12 5. Miami 3.1 11 6. St. Louis 2.7 7 4.1 18 7. Washington, DC The numbers of employees available for transfer from each of the current offices are as follows: Existing Office Available Employees Chicago Charlotte Pittsburgh Houston 24 19 16 21 The costs (in thousands of dollars) of transferring an employee from an existing office to a new office differ according to housing costs and moving expenses plus cost of living adjustments. They are as follows: Prospective New Offices (costs, $1,000s) Current Office 1. Atlanta 2. Boston 3. Denver 4. Detroit 5. Miami 6. St. Louis 7. Washington, DC 1. Chicago $19 $32 $27 $14 $23 $14 $41 2. Charlotte 14 47 31 28 35 18 53 3. Pittsburgh 16 39 26 23 31 19 48 4. Houston 22 26 21 18 28 24 43 The firm has ranked the possible new offices according to their profit potential, with Washington, DC, being the best (i.e., greatest potential), as follows: New Office Rank Atlanta S Boston 4 Denver 3 Detroit 1 Miami 6 St. Louis 2 Washington, DC 7 In addition, the firm wants at least one new office in the Midwest (i.e., Detroit and/or St. Louis) and exactly one new office in the Southeast (i.e., Atlanta or Miami). Formulate and solve a mixed integer programming model (binary and integer) to help Atlantic Systems determine how many new offices it should open, where they should be located, and how to transfer employees while maximizing total profit potential rank.