A store is known for is bargains. The store has the habit of lowering the price of its bargains each day, to ensure that articles are sold fast. Assume that you spot an item on Wednesday (there is only one of it left) that costs 30 Euro and that you would like to buy for a friend as present for Saturday. You know that the price will be lowered to 25 Euro on Thursday when the item is not sold, and to l0 Euro on Friday. You estimate that the probability that the item will be available on Thursday equals 0.7. You further estimate that assuming that it is still available on Friday when it was available on Thursday equals 0.6. You are sure that the item will no longer be available on Saturday. When you postpone your decision to buy the item to either Thursday or Friday, and the item is sold, you will buy another item of 40 Euro as present for Saturday.
a) Formulate the problem as stochastic dynamic programming problem. Specify phases, states, decisions and the optimal value function.
b) Draw the decision tree for this problem.
c) Give the recurrence relations for the optimal value function.
d) What is the minimal expected amount that you will pay for your present, and what is the optimal decision on Wednesday?