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.

 May 9, 2020
edited by boigotskills  May 9, 2020
edited by boigotskills  May 9, 2020

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.

 May 9, 2020

Here's a more detailed solution that agrees with Geno, that it isn't possible to do it within the specified cost:


 May 9, 2020

I think I get your solution, but is it possible to get the possible placement. I just need help with the placement. 

boigotskills  May 9, 2020

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