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4. (10 points) 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 preference among the five chores, as the following table shows: The parent's modest goal now is to finish as many chores as possible while abiding by the children's preferences. 1 Formulate, but do not solve, a binary programming problem to determine an assignment of chores to children that maximizes the number of preferred chores the children will do. 1 From Taha Operations Research an Introduction Ninth Edition