Direction: In the following figure that represents a network of roads, more than one road meets at intersections identified by numbers written on them. The traffic department is considering installation of surveillance cameras at these intersections that are capable of identifying all traffic violations on all the roads converging there. The cost of installing a surveillance camera at an intersection is equal to the intersection number (in lakhs of rupees). The Traffic Department wants all roads to be monitored at the minimum cost.
Statement 1 : It is more cost-effective to have surveillance cameras on intersections 2 and 4 than on intersections 7 and 3.
Statement 2 : Intersection 5 must have a surveillance camera.
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Which of the following is true?
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- Statement 1 is true but statement 2 is false.
- Statement 1 is false but statement 2 is true.
- Statement 1 is true and so is statement 2.
- Statements 1 and 2 are false.
Correct Option: C
As per the given conditions,
we require surveillance cameras that would cover all roads converging at an intersection. The cost for covering all the roads has to be minimum.
If we put a camera on ‘1’, roads from ‘7’ and ‘6’ to 1 will be covered.
If we put a camera on intersection ‘2’, roads converging from ‘3’ to ‘2’ will be covered.
If we put a camera on ‘3’, roads from ‘3’ to ‘5’, ‘6’ to ‘5’ and ‘7’ to ‘5’ will be covered.
Now we are left with roads from 7 to 4 and from 6 to 4 both of them converge from 4 hence these will be covered by putting a camera on ‘4’. And then all the roads will be covered and the minimum cost is 2 + 5 + 1 + 4 = 12 lakhs
