AMS 341 (Fall, 2023) Operations Research I: Deterministic Models Homework Set # 10
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AMS 341 (Fall, 2023)
Operations Research I: Deterministic Models
Homework Set # 10
Due on BrightSpace by 9am, Monday, December 11, 2023.
Read Sections 1,2,4,5 of Chapter 13 [WV] or 18 [W]. (you may skip parts on network representation).
Submit the following two problems:
(1). Use Dynamic Programming to solve the following: An airline plans to ly 6 lights out of Islip airport daily. There are 3 destinations under consideration, and each destination will have at most 3 lights to it. The proit is given in the table below. We wish to ind how many lights should be scheduled to each destination in order to maximize proit. We deine fi (s) as the maximum proit for destinations i, i + 1, ...3 with s lights to distribute.
destination |
1 light |
2 lights |
3 lights |
1 |
80 |
120 |
250 |
2 |
100 |
130 |
200 |
3 |
120 |
130 |
150 |
Solve using Dynamic Programming. Make sure to clearly deine 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 |
2023-12-28