The Father Domino Company sells copying machines. A major factor in making a sale is Domino$$s quick service. Domino sells copiers in six cities: Boston, New York, Philadelphia, Washington, Providence, and Atlantic City. The annual sales of copiers projected depend on whether a service representative is within $150$ miles of a city $($Table $1).$ Each copier costs $$500$ to produce and sells for $$1,000.$ The annual cost per service representative is $$80,000.$ Domino must determine in which of its markets to base a service representative. Only Boston, New York, Philadelphia, and Washington are under consideration as bases for service representative. The distance $($in miles$)$ between the cities is shown in Table $2.$

a$.$ Formulate a mathematical model that will help Domino maximize annual profits.

b$.$ Solve the mathematical model using LINGO.