A parent has five (teenage) children and five household chores to assign to them.

Past experience has shown that forcing chores on a child is counterproductive. With this in mind, the children are asked to list their preferences among the five chores, as the following table shows:

Child Preferred chore Rif 1, 3, 4, or 5 Mai 1 Ben 1 or 2 Kim 1, 2, or 5 Ken 2, 5 The parent’s modest goal now is to finish as many chores as possible while abiding by the children’s preferences. Determine the maximum number of chores that can be completed and the assignment of chores to children.