1. Every Saturday night a man plays poker, much to the dismay of his wife. Regardless of the mood his wife is in, if he takes her out to dinner (at a cost of $14 ), before going to play poker, she will be in a good mood with probability 7/8, and a bad mood with probability 1/8, next Saturday night. However, if he goes to play poker without taking her out to dinner first, she will be in a good mood next Saturday with probability 1/8, and a bad mood with probability 7/8, regardless of her mood this Saturday. Furthermore, if she happens to be in a bad mood and if he does not take her out to dinner, she will go to an exclusive store and buy an outfit at a cost of $75. Find the optimal policy that minimizes his expected discounted cost with a discount factor =0.8 using the linear programming method