Best location for a house
Alice owns a triangular parcel of land with a road on each edge of the parcel. There is occasional traffic of construction vehicles on each of the roads. She wishes to construct a house on the parcel with a driveway leading to each of the roads, paths leading to each corner of the lot, and an alarm at the house to signal a weather alert. Where should she locate the house to minimize the
a. sum of the lengths of the driveways?
b. longest driveway?
c. maximum noise heard at the house due to the trucks?
d. sum of the lengths of the paths?
e. power needed by the alarm that could be heard anywhere on the parcel?