Navarro_Priscilla_Homework04.docx - Priscilla Navarro MGMT...

Priscilla Navarro
MGMT 651 – Analytics for Managerial Decision-Making
Homework 4
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1. (15 points) Chapter 6 Problem 2
a. x
11
: Amount shipped from Jefferson City to Des Moines
x
12
: Amount shipped from Jefferson City to Kansas City
x
23
: Amount shipped from Omaha to St. Louis
Min 14 x
11
+ 9 x
12
+ 7 x
13
+ 8 x
21
+ 10 x
22
+ 5 x
23
x
11
+ x
12
+ x
13

30
x
21
+ x
22
+ x
23

20
x
11
+ x
21
= 25
x
12
+ x
22
= 15
x
13
+ x
23
= 10
x
11
, x
12
, x
13
, x
21
, x
22
, x
23
,  0
b. Optimal Solution:
Amount Cost ($)
Jefferson City - Des Moines 5 70
Jefferson City - Kansas City 15 135
Jefferson City - St. Louis 10 70
Omaha - Des Moines 20 160
Total 435
2. (15 points) Chapter 6 Problem 3
a.
1
Hamilton
3
Clermont
2
Butler
2
Northwest
1
Southern
10
20
15
12
15
18
400
200
300
500
400
Submit your homework as one single attachment. IncludePOM-QM input and output screenshots wherever
applicable. If you submit your homework as an MS-Excel document, make sure that it is properly
formatted to 8.5x11 page size!!
2 of 7

b. Let x
ij
= amount shipped from supply node i to demand node j .
Min 10 x
11
+ 20 x
12
+ 15 x
13
+ 12 x
21
+ 15 x
22
+ 18 x
23
s.t.
x
11
+ x
12
+ x
13

500
x
21
+ x
22
+ x
23

400
x
11
+ x
21
= 400
x
12
+ x
22
= 200
x
13
+ x
23
= 300
x
ij
 0 for all i , j
c. Optimal Solution
Amount Cost
Southern - Hamilton 200 $ 2000
Southern - Clermont 300 4500
Northwest - Hamilton 200 2400
Northwest - Butler 200 3000
Total Cost $11,900
d. The new optimal solution is:
Amount Cost
Southern - Hamilton 300 $ 3000
Southern - Clermont 300 4500
Northwest - Hamilton 100 1200
Northwest - Butler 300 4500
Total Cost $13,200
The new optimal solution is:
Amount Cost
Southern - Hamilton 200 $ 2000
Southern - Clermont 300 4500
Northwest - Hamilton 200 2400
Northwest - Butler 300 4500
Total Cost $13,400