B$)$ The Heartland Distribution Company is a food warehouse and distributor that has a contract with a grocer 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:

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$?$