As head of the engineering division of HP&L you have been asked to determine the least expensive way to add Bryan, Texas to the power grid, from Houston, Texas. Local substations lead from Houston to Bryan, and are currently on the grid, but if you use any of them them they will have to be modernized and upgraded at the following costs:
|
Location |
Cost to upgrade a station ($ million) |
|
|
Station 1 |
Houston |
1 |
|
Station 2 |
Somerville |
4 |
|
Station 3 |
Hearne |
7 |
|
Station 4 |
Tidwell |
11 |
|
Station 5 |
Athens |
8 |
|
Station 6 |
Pawnee |
5 |
|
Station 7 |
Bryan |
9 |
Costs for right-of-way acquisition, tower construction, and new line costs for connecting through any of the possible locations (in millions) are as shown below. If there is no station pair shown, you cannot acquire the right-of-way to connect between those stations. For example, it will cost you $6 million if you decide to string lines between Houston and Somerville (1-2), and you cannot acquire right-of-way between Houston and Tidwell, since 1-4 is not listed.
Line costs in $millions:
|
Between Station |
And Station |
Cost ($millions) |
|
1 |
2 |
6 |
|
2 |
4 |
5 |
|
4 |
5 |
3 |
|
5 |
7 |
11 |
|
1 |
7 |
32 |
|
1 |
6 |
8 |
|
6 |
7 |
9 |
|
1 |
3 |
12 |
|
3 |
5 |
10 |
|
2 |
3 |
6 |
Determine the least expensive way to connect Houston to Bryan.