(1). Use Dynamic Programming to solve the following: An airline plans to y 6 ights out of Islip airport daily. There are 3 destinations under consideration, and each destination will have at most 3 ights to it. The prot is given in the table below. We wish to nd how many ights should be scheduled to each destination in order to maximize prot. We dene f i (s) as the maximum prot for destinations i, i + 1, ...3 with s ights to distribute.

destination	1 ight	2 ights	3 ights
1 2 3	80 100 120	120 130 130	250 200 150

Solve using Dynamic Programming. Make sure to clearly dene the stages, the state and show your work.

(2). A company requires a certain machine for each of the next 6 years. It currently has one such machine. The cots of a new machine is $ 10,000. The operating cost and resale value of the machine are given in the table below. What is the replacement policy to minimize the cost of owning and operating a machine for the next 6 years? Show your work!

Age of machine	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6
Resale value Operating cost	7,000 300	6,000 500	4,000 800	3,000 1,200	2,000 1,600	1,000 2,200