2. [20 Pt.) The CBA Company is an organic food distributor that has a contract with a grocery store chain in several cities. The company plans to build new distribution centers in some of the cities....

2. [20 Pt.) The CBA Company is an organic food distributor that has a contract with a grocery store chain in several cities. The company plans to build new distribution centers in some of the cities. The company want the distribution centers to cover all the cities in which the grocery stores are located. A center can cover all stores within a radius of 250 miles. The company has a limited budget for its fixed annual costs as $1,900ks. The information about the estimated annual fixed cost for a distribution center in each city and the cities within 250 miles is given in the following table. Annual fixed cost ($1ks) 280 260 400 City 1. Atlanta 2. Charlotte 3. Cincinnati 4. Cleveland 5. Indianapolis 6. Louisville 7. Richmond 8. St. Louis 410 Cities within 250 miles 1, 2 1, 2,7 3, 4, 5, 6 3, 4, 5 3, 4, 5, 6,8 3, 5, 6, 8 2,7 5,6,8 290 370 390 300 Formulate a zero-one integer programming model to minimize the number of distribution centers to cover all the cities. 2.1) [5 Pt.] Define the decision variables. 2.2) [5 Pt.] Build the objective function. 2.3) (10 Pt.] Build the constraints.