A machine tool manufacturer is planning an expansion program. Up to 10 workers can be hired and assigned to the five divisions of the company. Since the manufacturer is currently operating with idle machine capacity, no new equipment has to be purchased. Hiring new workers adds $250/day to the indirect costs of the company. On the other hand, new workers add value to the company's output (i.e., sales revenues in excess of direct costs) as indicated in Table. Note that the value added depends upon both the number of workers hired and the division to which they are assigned.
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Table: Value added by new workers
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|
New worker (xn)
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Increase in contribution to overhead ($/day)
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|
Division 1
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Division 2
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Division 3
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Division 4
|
Division 5
|
|
0
|
0
|
0
|
0
|
0
|
0
|
|
1
|
30
|
25
|
35
|
32
|
28
|
|
2
|
55
|
50
|
65
|
60
|
53
|
|
3
|
78
|
72
|
90
|
88
|
73
|
|
4
|
97
|
90
|
110
|
113
|
91
|
|
5
|
115
|
108
|
120
|
133
|
109
|
|
6
|
131
|
124
|
123
|
146
|
127
|
|
7
|
144
|
133
|
135
|
153
|
145
|
|
8
|
154
|
140
|
140
|
158
|
160
|
|
9
|
160
|
150
|
144
|
161
|
170
|
|
10
|
163
|
154
|
145
|
162
|
172
|
The company wishes to hire workers so that the value that they add exceeds the $250/day in indirect costs. What is the minimum number of workers the company should hire and how should they be allocated among the five divisions?