I need help with this problem. It is pretty urgent. Please HeLp

[trashboi084]

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.

 

[Deleted member 4993]

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.

Note that towns A, B, C, D and the power stations are all on the East-West Highway. If I were to do this problem I would:

First plot on a line A, B, C & D and note there relative distances. Then I would choose one of those (A or B or C or D) as origin and locate the power plant at a distance 'p' from the origin.

Now calculate PA, PB, PC and PD.

Note that PA + PB + PC + PD ≤ 230

From this you should be able to calculate 'p'.
__________________________________________________________________
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[trashboi084]

@Subhotosh Khan, I am going to show you my solution. Please let me know if it is right.

Please let me know if I did it right? But, I still don't get the possible placement. I just need help finding the possible placement.

 

[Deleted member 4993]

@Subhotosh Khan, I am going to show you my solution. Please let me know if it is right.

Please let me know if I did it right? But, I still don't get the possible placement. I just need help finding the possible placement.

It is possible! Suppose I put :

the power plant at town A. How much total line is needed? (AB + AC + AD)

the power plant at town B. How much total line is needed? Continue.....

 

[Dr.Peterson]

@Subhotosh Khan, I am going to show you my solution. Please let me know if it is right.

Please let me know if I did it right? But, I still don't get the possible placement. I just need help finding the possible placement.

I came to the same conclusion, a slightly different way. I agree that there is no solution as the problem is stated. Maybe we're both reading it differently than Subhotosh.

 

[Deleted member 4993]

I came to the same conclusion, a slightly different way. I agree that there is no solution as the problem is stated. Maybe we're both reading it differently than Subhotosh.

Yes my solution to the problem was to string a power-line from A to D and then tap-out power for each town.

 

[trashboi084]

What do you mean by "tap-out power for each town?" Could you be a bit more specific?

 

[Dr.Peterson]

Yes my solution to the problem was to string a power-line from A to D and then tap-out power for each town.

The problem explicitly forbids that: "You must provide a separate cable connection from the power station to each town."

 

[trashboi084]

Wait. So if we are providing a separate cable connection, does that mean that there are no solutions to the problem, right?

 

[Deleted member 4993]

Wait. So if we are providing a separate cable connection, does that mean that there are no solutions to the problem, right?

Correct

 

[Deleted member 4993]

The problem explicitly forbids that: "You must provide a separate cable connection from the power station to each town."

I stand corrected - I missed that!