I'm trying to solve this problem:
An investment agency holds the rights to six investment projects: I1, I2, ..., I6. Projects I1, I2 and I3 are research and technological development projects and the remaining three, I4, I5 and I6, are sustainable agriculture projects. The agency intends to form portfolios consisting of a research and technological development project and a sustainable agriculture project. Due to the risk associated with the projects, only the following pairs of projects are feasible: (I1, I4), (I1, I5), (I2, I4), (I2, I5), (I2, I6), (I3, I4) (I3, I5) e (I3, I6). The risk associated to each project, measured on a scale of 0 -10 (0 - no risk; 10 - maximum risk), and the number of portfolios in which each project may be included are shown in the table below:
a) Represent the problem in a network and identify the network model that allows the agency to determine how many portfolios of two projects it will be possible to define. Justify
b) Suppose now that the agency wants to determine the three portfolios of two projects that minimise total risk. Indicate all the necessary changes to be made to the network shown in a) and state the network model that allows the optimal solution to be determined. Justify.
Point a) I considered that it was a problem of maximum flow and I solved it this way (but I don't know if it's right). M is considered to be a large number. Above the arcs are their capacities (in this case, it represents the number of portfolios).
I don't know how to solve part b) and turn the network in part a) into a minimum cost flow problem. I don't know where to put it on the network that I can only have 3 portfolios.