3. 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 $900,000. 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: Annual Fixed Charge ($1,000s) Cities Within 300 Miles City 1. Atlanta $276 2. Charlotte 253 3. Cincinnati 394 4. Cleveland 408 5. Indianapolis 282 6. Louisville 365 7. Nashville 268 8. Pittsburgh 323 9. Richmond 385 10. St. Louis 298 Atlanta, Charlotte, Nashville Atlanta, Charlotte, Richmond Cincinnati, Cleveland, Indianapolis, Louisville, Nashville, Pittsburgh Cincinnati, Cleveland, Indianapolis, Pittsburgh Cincinnati, Cleveland, Indianapolis, Louisville, Nashville, St. Louis Cincinnati, Indianapolis, Louisville, Nashville, St. Louis Atlanta, Cincinnati, Indianapolis, Louisville, Nashville, St. Louis Cincinnati, Cleveland, Pittsburgh, Richmond Charlotte, Pittsburgh, Richmond Indianapolis, Louisville, Nashville, St. Louis a. Formulate an integer programming model for this problem and solve it by using the computer. b. What is the solution if the cost constraint is removed from the original model formulation? What is the difference in cost?