A bookmaker has quoted odds on a tennis match between players I and II. The match consists of the best two out of three sets, i.e., if a player wins the rst two sets, the third set is not played and the bet on it is canceled. The bookmaker is giving odds of 5 to 2 that player I will win the match and odds of 3 to 2 that player I will win each set. A bettor has 100 dollars which he can distribute by betting on either player I or II to win the match and any of the sets. All bets are made before the match starts (if there are only two sets, all bets on the third set are returned to the bettor). (a) Find a way of placing bets so that no matter what happens the bettor is assured of winning an amount 2 where z is as large as possible. Formulate this problem as a linear programming and solve it using AMPL. (b) What if now we have best three out of ve sets, i.e., once a player wins three sets, no more sets are played and their correSponding bets are canceled, and everything else keeps the same? Resolve the problem and compare the answer with part (a)