$12\mathrm{.}4-7.$ An increasing number of Americans are moving to a warmer climate when they retire. To take advantage of this trend, Sunny Skies Unlimited is undertaking a major real estate devel$-$ opment project. The project is to develop a completely new re$-$ tirement community $($to be called Pilgrim Haven$)$ that will cover several square miles. One of the decisions to be made is where to locate the two fire stations that have been allocated to the com$-$ munity. For planning purposes, Pilgrim Haven has been divided into five tracts, with no more than one fire station to be located in any given tract. Each station is to respond to all the fires that occur in the tract in which it is located as well as in the other tracts that are assigned to this station. Thus, the decisions to be made consist of $(1)$ the tracts to receive a fire station and $(2)$ the assignment of each of the other tracts to one of the fire stations. The objective is to minimize the overall average of the response times to fires. SHIN The following table gives the average response time to a fire in each tract $($the columns$)$ if that tract is served by a station in a given tract $($the rows$).$ The bottom row gives the forecasted aver$-$ age number of fires that will occur in each of the tracts per day. Response Times $($in minutes$)$ Fire in Tract Assigned Station Located in Tract $123455201525102345124201525301562515201015$ A or $15251210512$ Average frequency of fires $2$ per $1$ per $1$ per $3$ per day day $3$ per day day day Formulate a BIP model for this problem. Identify any con$-$ straints that correspond to mutually exclusive alternatives or con$-$ tingent decisions.