John is travelling from home in Sydney to a hotel in Perth. Three stopovers on the way a number of choices of towns for each stop only one hotel to choose from in each town, except for Perth, where there are three hotels (J, K, and L) to choose from Each trip has a different distance resulting in a different cost (petrol) (cost is marked by each arc) Hotels have different costs (cost is marked by each node (town)) The goal is to select a route to and a hotel in Perth so that the overall cost of the trip is minimized. Use dynamic programming (forward recursion) to solve this problem by constructing the usual tables for each stage. Stage: (Sydney) Petrol cost start 22 8 Hotel cost 1 70 A 80 B C 80 25 10 2 50 D FR E 70 25 30 10 18 8 3 50 70 G 70 H I 60 8 20 10 10 10 10 50 4 (Perth) 15 13 K 10 15 L 60 70

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
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John is travelling from home in Sydney to a hotel in Perth.
Three stopovers on the way
a number of choices of towns for each stop
only one hotel to choose from in each town, except for Perth, where there are three hotels
(J, K, and L) to choose from
Each trip has a different distance resulting in a different cost (petrol) (cost is marked by each arc)
Hotels have different costs (cost is marked by each node (town))
●
●
●
The goal is to select a route to and a hotel in Perth so that the overall cost of the trip is minimized. Use
dynamic programming (forward recursion) to solve this problem by constructing the usual tables for each
stage.
Stage:
0 (Sydney) 1
Petrol cost
start
22
8
12
Hotel cost
70
80
B
80
25
10
2
50
A
E
70
30
10
18
8
7
3
50
F
70
70
H
60
8
10
10
4 (Perth)
50
13
K
10
15
L
60
70
Transcribed Image Text:John is travelling from home in Sydney to a hotel in Perth. Three stopovers on the way a number of choices of towns for each stop only one hotel to choose from in each town, except for Perth, where there are three hotels (J, K, and L) to choose from Each trip has a different distance resulting in a different cost (petrol) (cost is marked by each arc) Hotels have different costs (cost is marked by each node (town)) ● ● ● The goal is to select a route to and a hotel in Perth so that the overall cost of the trip is minimized. Use dynamic programming (forward recursion) to solve this problem by constructing the usual tables for each stage. Stage: 0 (Sydney) 1 Petrol cost start 22 8 12 Hotel cost 70 80 B 80 25 10 2 50 A E 70 30 10 18 8 7 3 50 F 70 70 H 60 8 10 10 4 (Perth) 50 13 K 10 15 L 60 70
Expert Solution
Step 1

To find:

The route and hotel in Perth so that the overall cost is minimized.

Given:

The number of stage is 4.

The Hotel cost is in red and petrol cost is in black.

 

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