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1. Solution:

A is correct. Note that there are 5 different paths from S to T that consist of three arcs:

                Dist
SADT      16
SACT      16
SCDT      23
SBCT      18
SBET      22

while there’s 1 path that consists of two arcs:

               Dist
SCT       16

Now, we won’t enumerate the paths that consist of more than four arcs, since these will involve paths that are longer given the following observations: once you are in node A, C or B, it is not optimal to go back to S since that will return you to your initial location. Once you are in D, there is no incentive going to C than directly going to T. The former has length 8 but the latter has length 7. Similarly, if you are in C, there is no incentive to go either D or E than directly going to T. This is also true if you are in E. Hence, given the table above, our solutions are SADT, SACT and SCT, which has length 16. Note that SADT is what is given in Choice A....

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