Ranchi city has only one fire station. The city$$s residents are very unhappy about this, so the city council has directed the city manager to develop a plan for locating multiple fire stations throughout the city. To get started, city manager divides the city into eight localities and then gathers data on estimated response time and cost related to acquiring the land and constructing a fire station $($see Table A$).$ The objective now is to determine which localities should receive a fire station to minimize the total cost of the stations while ensuring that each locality has at least one station close enough to respond to a fire in no more than $10$ minutes. Formulate the Linear Programming for this problem.

Table A: Response Time and Cost Data for the Ranchi City Problem

Response time $($min$.)$ for a fire in localities

Fire stations in localities $123456781$

$8$

$18$

$9$

$23$

$22$

$16$

$282$

$9$

$12$

$16$

$14$

$21$

$253$

$20$

$21$

$8$

$22$

$174$

$18$

$21$

$6$

$125$

$15$

$9$

$126$

$11$

$87$

$98$

Cost of station

$($ thousand$)$

$350$

$250$

$450$

$300$

$50$

$400$

$300$

$200$