. (20) The scheduling problem is a common variation of the assignment problem. In a schedul ing problem, we try to assign people to possible schedules in order to meet some require- ments. Suppose we are planning a board game mar in order to have enough players for each game. We are willing to bribe some of our friends with pizza to get them to come. Our marathon is going to last 5 hours and the number of players needed in each hour ih at for t -1,--. ,5 athon and need to get people to show ujp ? We have two types of friends: close friends and acquaintances. The acquaintances arrive anytime and stay for two hours (in a row), but need to leave before the 5th hour. We a need to provide less pizza (Since they aren't staying for dinner), so they only cost usci for the two hours they are present. Close triends stay for three hours in a row) and can arrive anytime after the 2nd hour (they are staying for dinner, so they want to come later in the evening). Our close friends are crazy board game fans and can play two games at once (which means they fill 2 of the as slots in hour t). However, we need to get more pizza for our close friends, so they cost us(C2> cover the three hours they are present. Finally, we are going to ask our friends to bring-beer to the party, and we want our average beer quality during the marathon to be at leas( ban arbitrary beer-rating scale). Close friends will bring beer of quality bc > b and acquaintances wl bring beer of quality ba