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.

$($a$)$ Formulate an integer programming model for this problem. write the objection function Z$=$x$1+$ x$2+$ x$3...$ etc and the constraints