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Elizabeth has convinced them that they can model the selection process with LP.
The LP will select the projects that maximize revenue while maintaining feasible
usage of resources; that is, the LP will not select a set of projects that consumes
more than the limited resources available, and it will do so while maximizing the
objective function (revenue).
In preparation for creating an LP, Elizabeth sets a project pricing policy that
estimates the revenue and outside resource usage associated with each project.
Although there are some variations in her estimates, the revenues and outside
resource usage are very nearly constant over short spans of time (3–6 months), cer-
tainly well within the quarterly planning horizon. The outside resources needed are
stated in terms of hours, and they represent hours of outside consulting that must
be obtained to perform a project. These include services like fieldwork by contract
archeologists, report writing, and other types of services. YRA has decided it is
wiser to obtain outside services than it is to hire permanent staff; it permits them
to be very agile and responsive to varying demand. We will assume four resource
types— Res-A , Res-B ,etc.
Exhibit 9.1 provides a convenient format for assembling the relevant data for
YRA’s project selection. For example, you can see that there are 25 projects of
Type 1 available in the quarter, and that each project produces revenue of $45,000.
The resources used in Type 1 projects are 6 hours of Res-A, 12 of Res-B, 0 of Res-
C, and 5 of Res-D. Note that there are seven types of projects available—Project 1,
Project 2, etc.
An examination of the data suggests that there is no possibility to accept all
projects, because doing so would result in a total of 5,432 hours. 2 Since there are
No.
Projects
Available
Project
Type
Total
Possible Rev
Res-A hrs.
used
Res-B hrs.
used
Res-C hrs.
used
Res-D hrs.
used
Rev.
1
25
45,000
1,125,000
6
12
0
5
2
30
63,000
1,890,000
9
16
4
8
3
47
27,500
1,292,500
4
10
4
5
4
53
19,500
1,033,500
4
5
0
7
5
16
71,000
1,136,000
7
10
8
4
6
19
56,000
1,064,000
10
5
7
0
7
36
48,500
1,746,000
6
7
10
3
Total Available
Total Resource Hrs. Available in Quarter
226
9,287,000
800
900
700
375
Exhibit 9.1 Projects for YRA budget
2 If we multiply the “No. Available” row by the individual “Res-A” through “Res-D” rows and
sum the results, we find that a total of 4400 hours would be required to satisfy all the available
projects. For example, for Res-A a total of 1338 hours would be required (6 25 + 9 30 + 47 4+
53 4+16 7+19 10 + 36 6
1338). Similarly, 2022, 929, and 1143 are needed for Res-B through
Res-D, respectively. Thus, 1338 + 2022 + 929 + 1143
=
=
5432.
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