Four workers are available to perform tasks 1-4. However, worker 1 can't do tasks 2, 3, or 4. Also, worker 2 can't do tasks 3 or 4 and worker 3 can't do tasks 1, 3, or 4. Worker 4 can do any task. Each worker can do at most one task, and each task should be performed at most once.

a) Draw the network for the maximum flow problem that can be used to determine whether all tasks can be assigned to a suitable worker. (Please specify the source and sink nodes, arc directions and arc capacities

b) Formulate this problem as a linear program. Clearly define all variables and constraints

c) Solve the model using Ford-Fulkerson algorithm (Please show all the iterations)

d) Use the final iteration of Ford-Fulkerson algorithm to find a minimum cut for this network and verify the strong duality (i.e, maximum flow = total capacity of the minimum cut).