Algebraic Formulation complete with objective function and constraint equations

7.11. 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 development project. The project is to develop a
completely new retirement 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 paramedic stations that have been allocated to the community to
respond to medical emergencies. For planning purposes, Pilgrim Haven has
been divided into five tracts, with no more than one paramedic station to be
located in any given tract. Each station is to respond to all the medical
emergencies 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 paramedic station and (2) the assignment of each of
the other tracts to one of the paramedic stations. The objective is to minimize
the overall average of the response times to medical emergencies.
The following table gives the average response time to a medical emergency
in each tract (the rows) if that tract is served by a station in a given tract (the
columns). The last column gives the forecasted average number of medical
emergencies that will occur in each of the tracts per day.
Formulate and solve a BIP model on a spreadsheet for this problem. Identify
any constraints that correspond to mutually exclusive alternatives or contingent
decisions.

Paramedic Station in Tract Average Frequency of Medical Emergencies 2 W 4 5 per Day Response 5 20 15 25 10 times (min.) 12 4 15 to a medcal U A W N- 30 15 25 U -U-N emergency 20 10 15 12 In tract 15 25 12 10 5