(20 points) Problem 6-35, page 267. First, draw the network with nodes, arcs, and are capacities that corresponds to this problem, and then use the maximum flow algorithm to solve it. Then write out your interpretation of the solution you obtain. In your assignment of chores to children, which child does which chore? Are any chores left undone? Are any children left without a chore? Note: Each child can only do at most one chore, and each chore can be done by at most one child. You may assume that when a child prefers more than one chore (such as Rif, for example), that he or she prefers each of them equally. 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 Mai Ben Kim Ken 3,4, or 5 1 1 or 2 1, 2, or 5 2 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