A recent tragic fire in Carbonville, Illinois, has prompted the City Council to draft a new ordinance requiring all buildings to have fully operational sprinkler systems installed by the end of the...

A recent tragic fire in Carbonville, Illinois, has prompted the City Council to draft a new ordinance requiring all buildings to have fully operational sprinkler systems installed by the end of the year. The Talcon Building is affected by this ordinance. From the original blueprints, engineers have designed positions for the location of eight powerful sprinkler heads that are to be connected to the sprinkler controller. The feasible connections between these eight sprinkler heads and the controller with distance shown in feet are depicted in the figure for problem 4.

a. What design of the sprinkler system will minimize the total amount of pipe required (and hence give the maximal water pressure throughout the system)?

 b. Suppose the engineers discovered that the connection between Office #1 and the Storage Room could not be made because of a recently installed air conditioning duct. What design of the sprinkler system would now minimize the total amount of pipe required? * * 5