A construction company has four projects in progress. According to the current allocation of manpower, equipment, and materials, the four projects can be completed in 15, 20, 18, and 25 weeks. Management wants to reduce the completion times and has decided to allocate an additional $35,000 to all four projects. The new completion times as functions of the additional funds allocated to each projects are given in Table.
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Table: Completion Times (in weeks)
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Additional funds (x1000 dollars)
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Project 1
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Project 2
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Project 3
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Project 4
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0
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15
|
20
|
18
|
25
|
|
5
|
12
|
16
|
15
|
21
|
|
10
|
10
|
13
|
12
|
18
|
|
15
|
8
|
11
|
10
|
16
|
|
20
|
7
|
9
|
9
|
14
|
|
25
|
6
|
8
|
8
|
12
|
|
30
|
5
|
7
|
7
|
11
|
|
35
|
4
|
7
|
6
|
10
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How should the $35,000 be allocated among the projects to achieve the largest total reduction in completion times? Assume that the additional funds can be allocated only in blocks of $5000.