10.3-3. At a small but growing airport, the local airline company is purchasing a new tractor for a tractor-trailer train to bring luggage to and from the airplanes. A new mechanized luggage system will be installed in 3 years, so the tractor will not be needed after that. However, because it will receive heavy use, so that the running and maintenance costs will increase rapidly as the tractor ages, it may still be more Page 415 economical to replace the tractor after 1 or 2 years. The following table gives the total net discounted cost associated with purchasing a tractor (purchase price minus trade-in allowance, plus running and maintenance costs) at the end of year i and trading it in at the end of year j(where year 0 is now). 1 2 3 0 $8,000 $18,000 $31,000 1 10,000 21,000 2 12,000 The problem is to determine at what times (if any) the tractor should be replaced to minimize the total cost for the tractors over 3 years. (a) Formulate this problem as a shortest-path problem. (b) Use the algorithm described in Sec. 10.3 to solve this shortest-path problem.
10.3-3. At a small but growing airport, the local airline company is purchasing a new tractor for a tractor-trailer train to bring luggage to and from the airplanes. A new mechanized luggage system will be installed in 3 years, so the tractor will not be needed after that. However, because it will receive heavy use, so that the running and maintenance costs will increase rapidly as the tractor ages, it may still be more Page 415 economical to replace the tractor after 1 or 2 years. The following table gives the total net discounted cost associated with purchasing a tractor (purchase price minus trade-in allowance, plus running and maintenance costs) at the end of year i and trading it in at the end of year j(where year 0 is now). 1 2 3 0 $8,000 $18,000 $31,000 1 10,000 21,000 2 12,000 The problem is to determine at what times (if any) the tractor should be replaced to minimize the total cost for the tractors over 3 years. (a) Formulate this problem as a shortest-path problem. (b) Use the algorithm described in Sec. 10.3 to solve this shortest-path problem.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:10.3-3. At a small but growing airport, the local airline company is purchasing a new
tractor for a tractor-trailer train to bring luggage to and from the airplanes. A new
mechanized luggage system will be installed in 3 years, so the tractor will not be needed
after that. However, because it will receive heavy use, so that the running and
maintenance costs will increase rapidly as the tractor ages, it may still be more Page 415
economical to replace the tractor after 1 or 2 years. The following table gives
the total net discounted cost associated with purchasing a tractor (purchase price minus
trade-in allowance, plus running and maintenance costs) at the end of year i and trading it
in at the end of year j(where year 0 is now).
,
1
2
3
0
$8,000
$18,000
$31,000
1
10,000
21,000
2
12,000
The problem is to determine at what times (if any) the tractor should be replaced to
minimize the total cost for the tractors over 3 years.
(a) Formulate this problem as a shortest-path problem.
(b) Use the algorithm described in Sec. 10.3 to solve this shortest-path problem.
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