Suggested Problem Set 6 - Deterministic Dynamic Programming PDF

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Suggested Problem Set 6 -Deterministic Dynamic Programming...

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Suggested Problems 6

1. The owner of a chain of three grocery stores has purchased five crates of fresh strawberries. The estimated probability distribution of potential sales of the strawberries before spoilage differs among the three stores. Therefore, the owner wants to know how to allocate five crates to the three stores to maximize expected profit. For administrative reasons, the owner does not wish to split crates between stores. However, he is willing to distribute no crates to any of his stores. The following table gives the estimated expected profit at each store when it is allocated various numbers of crates:

Crates 0 1 2 3 4 5

1 0 5 9 14 17 21

Store 2 0 6 11 15 19 22

3 0 4 9 13 18 20

Use dynamic programming to determine how many of the five crates should be assigned to each of the three stores to maximize the total expected profit.

2. (Problem 12-2, page 465 in text) I am an avid hiker. Last summer, my friend G. Don and I went on a 5-day hike-and-camp trip in the beautiful White Mountains in New Hampshire. We decided to limit our hiking to an area comprising three well-known peaks: Mounts Washington, Jefferson, and Adams. Mount Washington has a 6-mile base-to-peak trail. The corresponding base-to-peak trails for Mounts Jefferson and Adams are 4 and 5 miles, respectively. The (two-way) trails joining the bases of the three mountains are 3 miles between Mounts Washington and Jefferson, 2 miles between Mounts Jefferson and Adams, and 5 miles between Mounts Adams and Washington. We started on the first day at the base of Mount Washington and returned to the same spot at the end of 5 days. Our goal was to hike as many miles as we could. We also decided to climb exactly one mountain each day and to camp at the base of the mountain we would be climbing the next day. Additionally, we decided that the same mountain could not be visited in any two consecutive days. Use DP to plan the 5-day hike....