Figure $3$: The graph for Question $4.$ The nodes on the left are the

students, the nodes on the right are the assignment problems, and the

edges indicate the preferred tasks for each student.

Six students are working on a group project. The project is di$-$

vided into six tasks, so the students decide that each person will

be responsible for one task. Each student nominates two or three

preferred tasks, as shown in Figure $3.$

Use the Hungarian algorithm to ensure that each student is as$-$

signed to one of their preferred tasks. Start the algorithm with an

empty matching and clearly explain how the algorithm progresses.

When implementing the algorithm, progress through the nodes sys$-$

tematically. Draw a graph of your solution.