1. The Hatfields, Montagues, Dourmayeur, and Capulets are going on their annual family picnic (call them family 1 , family 2 , family 3 , family 4 , respectively). Four cars are available to transport the families to the picnic. Any family member that does not fit in one of the cars, we have to order a special limousine for them (aka it's expensive). Therefore, we want to fit as many family members into these cars. Due to interfamily disputes, each of the four cars allow only members of 2 of the families. Car 1 allows members from family 1 and 2. Car 2 allows members from family 1 and 3 . Car 3 allows members from family 2 and 3. Car 4 allows members from family 3 and 4 . This information and the capacities of the cars are given in the table below. FAMILY INFORMATION CAR INFORMATION (a) Formulate the problem of transporting the maximum possible number of people using these four cars to the picnic as a maximum-flow problem. (b) Now, solve this problem and find the maximum flow. List the augmenting paths you used in solving the problem in the format below. Also, show the minimum cut by identifying the nodes of the source set. There are multiple ways to solve this (you may need more or less lines than what is given here). Minimum cut (set of nodes that belong to source set)