CarpetPlus sells and installs floor covering for commercial buildings. Brad Sweeney, a CarpetPlus account executive, was just awarded the contract for five jobs. Brad must now assign a CarpetPlus installation crew to each of the five jobs. Because the commission Brad will earn depends on the profit CarpetPlus makes, Brad would like to determine an assignment that will minimize total installation costs. Currently, five installation crews are available for assignment. Each crew is identified by a color code, which aids in tracking of job progress on a large white board. The following table shows the costs (in hundreds of dollars) for each crew to complete each of the five jobs:
| |
|
1
|
2
|
Job 3
|
4
|
5
|
|
Red
|
30
|
44
|
38
|
47
|
31
|
|
White
|
25
|
32
|
45
|
44
|
25
|
|
Crew
|
Blue
|
23
|
40
|
37
|
39
|
29
|
|
|
Green
|
26
|
38
|
37
|
45
|
28
|
|
|
Brown
|
26
|
34
|
44
|
43
|
28
|
a. Develop a network representation of the problem.
b. Formulate and solve a linear programming model to determine the minimum cost assignment.