The State wants to build a power station along an East-West highway to supply power
to four small towns, A, B, C, & D located along the highway. Town C is 100 miles West
of D and 85 miles East of B. Town A is 30 miles West of B. The cost of connecting the
power station to any town in $1000 per mile of cable. The total budget cannot exceed
$230,000. Where can the power station be located? You must provide a separate cable
connection from the power station to each town.
If these towns are in a straight East-West line, then, from West to East are:
A -- 30 miles -- B -- 85 miles -- C -- 100 miles -- D
If you must connect each of these by a separate calbe to a power station (at $1000 per mile),
-- if you place the power station at B or C or anywhere between B and C, the total cost will be $300,000.
-- if you place the power station either west of B or east of C, the total cost will be higher.
So, if I am reading the question correctly, I can't solve the problem.
I am interested to see anyone else's solution.