Question

Below is the linear programming for the Shortest Path Problem.

Considering the second contraint in the mathematical model :

∑ixji−∑ixij=0∀j≠s,j≠t

What is the logic behind this contraint?

To make sure there is only one solution

To make sure that the path is connected between the nodes

To make sure the variable stays binary

This contraint is redundant and not necessary

Which of the following statements are true? (select all that apply)

The shape of a student t-distribution curve depends on its degrees of freedom

If a set of random variables are mutually exclusive, this means they are independent and identically distributed

For a sample of size 30, if c is the confidence level and L is the confidence interval, increasing the confidence level c leads to a narrower confidence interval L

Well connected cities have a lower circuity factor compared to the cities with mountain ranges

unanswered

Answer 1

1.

The above constraint makes sure that the number of paths going into a node-j (all the intermediate nodes) equals the number coming out i.e. in other words, To make sure that only one arc goes into a node and just one comes out leading to make sure that the path is connected between the nodes.

2.

Option-1: The nature of t-distribution is defined by the degrees of freedom - So, CORRECT
Option-2: Mutually exclusive imply that the events are not independence - So, INCORRECT
Option-3: As confidence level increases, the confidence interval must be wider, e.g. I am 100% confident that your height is between 0 to 10 ft. But I might be 95% confident that your highest is between 5 ft and 6 ft. - So, INCORRECT
Option-4: The circuitry factor is the ratio of the actual network distance divided by the euclidean distance, this should be more in the mountain area compared to the connected cities - So, CORRECT