Reconsider Prob. $12\mathrm{.}2-4.$ 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 min$-$

imize 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 neces$-$

sary to assign this tract to just one of these stations.