For the problem below: first, set up the problem for solution by dynamic programming and answer the following questions:

• what are the stages in this problem?

• what defines the states within each stage?

• for each stage-state combination, what are the decisions you are choosing between?

• what is the interpretation of the value function f(i) for this particular problem?

next, solve the problem by hand using dynamic programming, showing your work. state the optimal expected value.

problem 1: selling t-shirts you have a sideline business selling t-shirts at university football games. you are equally likely to sell 200 or 400 t-shirts at each game. each time you place an order you pay $500 plus $5 for each t-shirt you order. each t-shirt sells for $8. a holding cost of $2 per t-shirt is assessed against each t-shirt left at the end of the game includes storage costs and the cost of capital tied up in unsold merchandise).
you can store at most 400 t-shirts after each game.
assuming that the number of t-shirts in any of your orders must be a multiple of 100, determine an optimal ordering policy that maximizes your expected profits earned during the first three games of the season.
assume that any leftover t-shirt has a value of $6.