Formulate this problem as an LP (đo not solve. Just ABC company produces and sells wooden desks. The demand is forecasted for each month of the next year. The company currently has 20 employees and each employee can produce 30 desks in a month. The monthly salary of each employee is $110. Since raw material cost change at each month, the production costs are different for each month of the year. Excessive amount produced in a month can be stored in the inventory for use in the following months. However, the storage space has a capacity of 300 desks in total. The inventory holding costs are also different at each month. In order to satisfy excessive demand in a month, the company may use its inventories, may implement overtime working hours, or hire additional workers. The total overtime production for each worker at each month can be at most 10% of the regular time production. Also the overtime production cost is different than the regular time production cost. Furthermore, the maximum number of workers who can work in the company at the same time is 25. It is also possible to fire the workers but the workforce cannot be less than 15. Hiring and firing costs differ each month. The objective function is to minimize the total cost.

Practical Management Science
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ISBN:9781337406659
Author:WINSTON, Wayne L.
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Chapter3: Introduction To Optimization Modeling
Section3.8: A Multiperiod Production Model
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Please formulate this problem as an LP. (Just formulation). 

Formulate this problem as an Lp (do not solve. Just formulate)
ABC company produces and sells wooden desks. The demand is forecasted for each month of the next
year. The company currently has 20 employees and each employee can produce 30 desks in a month.
The monthly salary of each employee is $110. Since raw material cost change at each month, the
production costs are different for each month of the year. Excessive amount produced in a month can
be stored in the inventory for use in the following months. However, the storage space has a capacity of
300 desks in total. The inventory holding costs are also different at each month. In order to satisfy
excessive demand in a month, the company may use its inventories, may implement overtime working
hours, or hire additional workers. The total overtime production for each worker at each month can be
at most 10% of the regular time production. Also the overtime production cost is different than the
regular time production cost. Furthermore, the maximum number of workers who can work in the
company at the same time is 25. It is also possible to fire the workers but the workforce cannot be less
than 15. Hiring and firing costs differ each month. The objective function is to minimize the total cost.
Transcribed Image Text:Formulate this problem as an Lp (do not solve. Just formulate) ABC company produces and sells wooden desks. The demand is forecasted for each month of the next year. The company currently has 20 employees and each employee can produce 30 desks in a month. The monthly salary of each employee is $110. Since raw material cost change at each month, the production costs are different for each month of the year. Excessive amount produced in a month can be stored in the inventory for use in the following months. However, the storage space has a capacity of 300 desks in total. The inventory holding costs are also different at each month. In order to satisfy excessive demand in a month, the company may use its inventories, may implement overtime working hours, or hire additional workers. The total overtime production for each worker at each month can be at most 10% of the regular time production. Also the overtime production cost is different than the regular time production cost. Furthermore, the maximum number of workers who can work in the company at the same time is 25. It is also possible to fire the workers but the workforce cannot be less than 15. Hiring and firing costs differ each month. The objective function is to minimize the total cost.
Current
Production
Max.
Storage
Сарacity
Employe
Number of Min Number Salary of
Workers
per
es
Employee
of Workers employees
20
30
300
25
15
110
Inventory
Holding
Cost
Overtime
Production
Production
Firing
Hiring Cost
192
Month
Demand
Cost
Cost
Cost
1
520
8
1
9
312
850
7
8
294
276
670
4
5
300
342
710
2
4
3
282
306
520
6
3
7
276
222
660
8.
3
9
144
294
300
2
9
240
180
400
1
7
252
190
9
470
7
4
8
162
200
10
760
7
5
8
228
200
11
610
4
210
210
12
900
8.
1
9
192
240
43
Transcribed Image Text:Current Production Max. Storage Сарacity Employe Number of Min Number Salary of Workers per es Employee of Workers employees 20 30 300 25 15 110 Inventory Holding Cost Overtime Production Production Firing Hiring Cost 192 Month Demand Cost Cost Cost 1 520 8 1 9 312 850 7 8 294 276 670 4 5 300 342 710 2 4 3 282 306 520 6 3 7 276 222 660 8. 3 9 144 294 300 2 9 240 180 400 1 7 252 190 9 470 7 4 8 162 200 10 760 7 5 8 228 200 11 610 4 210 210 12 900 8. 1 9 192 240 43
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ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,