Reconsider Prob. $12\mathrm{.}4-7.$ The management of Sunny Skies Unlimited now has decided that the decision on the locations of the fire stations should be based mainly on costs. The cost of locating a fire station in a tract is $$200,000$ for tract $1,$ $$250,000$ for tract $2,$ $$400,000$ for tract $3,$ $$300,000$ for tract $4,$ and $$500,000$ for tract $5.$ Management's objective now is the following Determine which tracts should receive a station to minimize the total cost of stations while ensuring that each tract has at least one station close enough to respond to a fire in no more than $15$ minutes $($on the average$).$ In contrast to the original problem, note that the total number of fire stations is no longer fixed Furthermore, if a tract without a station has more than one station within $15$ minutes, it is no longer necessary to assign this tract to just one of these stations. $($a$)$ Formulate a complete pure BIP model with $5$ binary variables for this problem $($b$)$ Is this a set covering problem? Explain, and identify the relevant sets $($c$)$ Use the computer to solve the model formulated in part $($a$).$