2. [30 Pt.] [DO NOT USE EXCEL TO SOLVE THIS PROBLEM.] [SHOW FORMULATIONS BELOW by ANSWERING al, a2 and a3.] The Heartland Distribution Company is a food warehouse and distributor that has a contract with a grocery store chain in several Midwest and Southeast cities. The company wants to construct new warehouses/distribution centers in some of the cities it services to serve the stores in those cities plus all the other stores in the other cities that don't have distribution centers. A distribution center can effectively service all stores within a 300-mile radius. The company also wants to limit its fixed annual costs to under $1,200,000. The company wants to build the minimum number of distribution centers possible. The following table shows the cities within 300 miles of every city and the projected fixed annual charge for a distribution center in each city. City 1. Atlanta 2. Charlotte 3. Cincinnati 4. Cleveland 5. Indianapolis 6. Louisville 7. Nashville 8. Pittsburgh 9. Richmond 10. St. Louis Annual fixed charge ($1ks) 280 260 400 410 290 370 270 330 390 300 Cities within 300 miles 1, 2, 7 1, 2,9 3, 4, 5, 6, 7, 8 3, 4, 5, 8 3, 4, 5, 6, 7, 10 3, 5, 6, 7, 10 1, 3, 5, 6, 7, 10 3, 4, 8, 9 2, 8, 9 5, 6, 7, 10 a) Formulate a model for this problem. al) [5] Define decision variables a2) [10] Define objective function a3) [15] Define the constraints