Bob has a concession at yankee stadium. he can sell 500 umbrellas at exist10 each if it rains. (the umbrellas cost him exist5 each.) if it shines, he can sell only 100 umbrellas at exist10 each and 1000 sunglasses at exist5 each. (the sunglasses cost him exist2 each.) he has exist2500 to invest in one day, but everything that isn't sold is trampled by the fans and is a total loss. this is a game against nature. nature has two strategies: rain and shine. bob also has two strategies: buy for rain or buy for shine. find the optimal strategy for bob assuming that the probability for rain is 50%.