Answer to Homework Chapter 10
BSNS2120, J. Wang
P.456 –
#17.
Module/submodule: Transportation
Problem title: Problem #17
Starting method: Any starting method
Objective: Minimize
Original Data
Coal
Coal Valley Coaltown
Junction
Coalsburg
SUPPLY
----------------------------------------------------------------------------Morgantown
50
30
60
70
35
Youngstown
20
80
10
90
60
Pittsburgh
100
40
80
30
25
DEMAND
30
45
25
20
Optimal Solution – The best shipment arrangement:
Coal
Coal Valley Coaltown
Junction
Coalsburg
---------------------------------------------------------------Morgantown
35
Youngstown
30
5
25
Pittsburgh
5
20
Optimal total cost = 3,100
(a) 25 cars should be shipped from Youngstown to Coal Junction.
(b) Yes, Coaltown’s demand of 45 cars is satisfied. Among the cars shipped to Coaltown, 35 are
from Morgantown, 5 from Youngstown, and 5 from Pittsburgh.
(c) The minimized total cost is 3,100. The label of the total cost in this problem is “mile”. That is,
the minimized cost is 3,100 miles of shipping in total.
#21.
Module/submodule: Transportation
Problem title: Problem #21
Demand, supply, and shippment are in terms of “million-kilowatt-hours”.
Cost is in terms of “million-cents”.
Objective: Minimize
Original Data
W
X
Y
Z
SUPPLY
----------------------------------------------------------------A
12
4
9
5
55
B
8
1
6
6
45
C
1
12
4
7
30
DEMAND
40
20
50
20
Optimal Solution – The best shipment arrangement:
W
X
Y
Z
-----------------------------------------------------A
35
20
B
10
20
15
C
30
Optimal total cost = 635
(a) 20 million-kilowatt-hours should be shipped from A to Z.
(b) Companies W, X, and Y will receive power from B.
(c) The minimized cost is 635. The label of the total cost is “million-cents”.
(d) The minimized total cost in terms of dollar is 635 X 1,000,000 / 100 = $6,350,000.
#22.
Module/submodule: Transportation
Problem title: Problem #22
Starting method: Any starting method
Objective: Minimize
Original Data
Destination Destination Destination
A
B
C
SUPPLY
-------------------------------------------------------------Source 1
8
9
4
72
Source 2
5
6
8
38
Source 3
7
9
6
46
Source 4
5
3
7
19
DEMAND
110
34
31
Optimal Solution – The best shipment arrangement:
Destination Destination Destination
A
B
C
------------------------------------------------Source 1
41
31
Source 2
23
15
Source 3
46
Source 4
19
Optimal total cost = $1,036
#23.
Module/submodule: Transportation
Problem title: Problem #23
Starting method: Any starting method
Objective: Minimize
Original Data
Hospital 1 Hospital 2 Hospital 3 Hospital 4
SUPPLY
----------------------------------------------------------------Bank 1
8
9
11
16
50
Bank 2
12
7
5
8
80
Bank 3
14
10
6
7
120
DEMAND
90
70
40
50
Optimal Solution – The best shipment arrangement:
Hospital 1 Hospital 2 Hospital 3 Hospital 4
-----------------------------------------------------Bank 1
50
Bank 2
10
70
Bank 3
30
40
50
Optimal total cost = $2,020
#30.
(a)
Module/submodule: Assignment
Problem title: Problem 30
Objective: Minimize
Original Data
W
X
Y
Z
-----------------------------------------------------A12
10
14
16
13
A15
12
13
15
12
B2
9
12
12
11
B9
14
16
18
16
The optimal solution: - the best assignments:
W
X
Y
Z
-----------------------------------------------------A12
ASSIGN
A15
ASSIGN
B2
ASSIGN
B9
ASSIGN
Optimal total cost = 50
(b)
Module/submodule: Transportation
Problem title: Problem 30
Objective: Minimize
Original Data
W
X
Y
Z
SUPPLY
----------------------------------------------------------------A12
10
14
16
13
1
A15
12
13
15
12
1
B2
9
12
12
11
1
B9
14
16
18
16
1
DEMAND
1
1
1
1
The optimal solution: - the best assignments:
W
X
Y
Z
-----------------------------------------------------A12
1
A15
1
B2
1
B9
1
Optimal total cost = 50
(c) Job A15 should be done on machine Z.
(d) The total minimized cost of doing four jobs is 50. The label of the cost is “hour”. That is, the
optimal cost is 50 hours to finish the four jobs.
#32.
Module/submodule: Assignment
Problem title: Problem 32
Objective: Minimize
Original Data
Kansas
City
Chicago
Detroit
Toronto
------------------------------------------------------Seattle
1500
1730
1940
2070
Arlington
460
810
1020
1270
Oakland
1500
1850
2080
999999
Baltimore
960
610
400
330
The optimal solution: - the best assignments:
Kansas
City
Chicago
Detroit
Toronto
------------------------------------------------------Seattle
ASSIGN
Arlington ASSIGN
Oakland
ASSIGN
Baltimore
ASSIGN
Optimal total cost = 4,580
(a) Empire of the Chicago game comes from Oakland.
(b) The total minimized cost is 4,580. The label of the cost is “mile” or “driving mileage”. That is,
the optimal cost is 4,580 driving mileages in total for the four empires.