Direction: A significant amount of traffic flows from point S to point T in the one-way street network shown below.
Points A, B, C and D are junctions in the network, and the arrows mark the direction of traffic flow.
The fuel cost in rupees for travelling along a street is indicated by the number adjacent to the arrow representing the street.
Motorists travelling from point S to point T would obviously take the route for which the total cost of travelling is the minimum.
If two or more routes have the same least travel cost, then motorists are indifferent between them.
Hence, the traffic gets evenly distributed among all the least cost routes The government can control the flow of traffic only by levying appropriate toll at each junction.
For example, if a motorist takes the route S - A - T (using junction A alone), then the total cost of travel would be Rs 14 (i.e. Rs 9 + Rs 5) plus the toll charged at junction A.
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The government wants to devise a toll policy such that the total cost to the commuters per trip is minimized. The policy should also ensure that not more than 70 percent of the total traffic passes through junction B. The cost incurred by the commuter travelling from point S to point T under this policy will be:
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- $ 7
- $ 9
- $ 10
- $ 13
- $ 14
Correct Option: C
On the basis of above given question , we can say that
There must be one other route other than those involving B.
We must take S - D - C - T as the other route.
S - B - C - T, if toll at B = 3, total cost = 10
S - D - C - T, if toll at D and C is 0, total cost is 10.
Hence ,$ 10 is the least cost.
