Consider a network with 3 nodes A,B,C, and three links that form a triangle. Links AB and BC have capacity 3, while link CA has capacity 6. There are 5 fows with the paths indicated: Flow 1 (AB), Flow 2 (AB), Flow 3 (ABC), Flow 4 (BCA), Flow 5 (CA). For each of the following performance criteria, determine the values for the rates xi of the 5 flows, as well as the resulting total throughput. (a) maxmin (b) proportional fair (c) minimum potential delay (all weights equal to one) (d) maxmin but with the additional constraint that x1 0.5-i.e., user 1 has no use for more than a rate of 0.5. NOTE: When there are upper limit constraints, you can solve using the waterfilling procedure, but with the modification that when the rate for a flow reaches its upper limit, the rate for that .flow no longer continues to be increased. When there are upper limit constraints, maxmin means that we are maximizing the minimum rate among the users who get less than the rate they request. (e) maxmin but with the additional constraints that x1 0.5 and x2 0.75.