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MIE376: DP Problems
1.
Consider the network below, where the numbers on each arc represent the distance between the nodes. Find the shortest path in
the network using dynamic programming.
5
9
6
7
6
8
7
7
6
2.
The owner of a chain of three grocery stores has purchased five crates of fresh strawberries. The following table gives the
estimated expected profit at each store when it is allocated various number of crates:
Number of crates
Store 1
Store 2
Store 3
0
0
0
0
1
5
6
4
2
9
11
9
3
14
15
13
4
17
19
18
5
21
22
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. Note: Crates cannot be split among stores.
3.
City planners are to recommend the “best” allocation of fire stations to three districts. Anywhere from zero to three stations can
be located in a district. The number of stations located in a district has a bearing on the annual property damage caused by fires
for that district. The table below reflects this relationship. A budget constraint restricts the total number of allocations to five
stations.
Annual Property Damage (in millions of dollars)
District
Number of stations per district
0
1
2
3
A
2.0
0.9
0.3
0.2
B
0.5
0.3
0.2
0.1
C
1.5
1.0
0.7
0.3
a)
Identify the Dynamic Programming Structure (i.e. stages, states, etc.)
b)
Determine the optimal allocation by DP
4.
A farmer owns K sheep. At the end of each year, a decision is made as to how many to sell or keep. The profit from selling a
sheep in year n is p
n
. The sheep kept in year n will double in number in year n+1. The farmer plans to sell out completely at the
end of N years.
a.
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 Spring '11
 Daniel

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