The state of Missouri has three major power-generating companies (A, B and C). During the months of peak demand, the Missouri Power Authority authorizes these companies to pool their excess supply and to distribute it to smaller independent power companies that do not have generators large enough to handle the demand. Excess supply is distributed on the basis of cost per kilowatt-hour transmitted. The following table shows the demand and supply in millions of kilowatt hours and the costs per kilowatt hour of transmitting electric power to four small companies in cities, W, X, Y and Z:
|
To From
|
W
|
X
|
Y
|
Z
|
Excess Supply
|
|
A
|
$12
|
$4
|
$9
|
$5
|
55
|
|
B
|
8
|
1
|
6
|
6
|
45
|
|
C
|
1
|
12
|
4
|
7
|
30
|
|
Unfilled Power Demand
|
40
|
20
|
50
|
20
|
|
The Company wishes to minimize its total transportation costs.
Find the least-cost distribution system.