4. [8 marks] A company needs to assign certain roles to members of its staff. Only some of the staff are able to perform any given role; these staff capabilities could be summarized in a table like this one. Admin Designer Manager Programmer Salesperson Bob Yes Yes No No No Cheung Yes No No No No Emily Yes No Yes Yes No Fatima No Yes No No Yes Construct a directed graph in which the vertices consist of: a source A, a sink Z, the staff members, and the roles. There is an arc from A to each staff member, and from each role to the sink; and there is an arc from staff member W to role R if and only if W can perform R. Set the capacity of every arc to be 1 Let f be a flow in this network. If f assigns value 1 to the arc from a worker W to role R, we assign W to the role R. (a) Explain carefully what the various conditions for a flow tell you about these assignments. (b) Find a maximal flow in the network. (c) What does this tell you