(25p) Four families, The Hatfields, Montagues, McCoys, and Capulets, are going on their annual family picnic. Four cars are available to transport the families to the picnic. The cars can carry the following number of people: car 1, four; car 2, three; car 3, three; and car 4, four. There are four people in each family, and no car can carry more than two people from any one family. The aim is to determine the maximum possible number of people that can be transported to the picnic. This problem can be formulated as a maximum-flow problem.
a) (10p) Draw a network that represents this problem.
b) (10p) Formulate this problem as a linear programming model.
c) (5p) Solve the LP using an appropriate solver. What is the optimal transportation plan?