The production manager of Videotechnics Company is attempting to determine the u
ID: 3005298 • Letter: T
Question
The production manager of Videotechnics Company is attempting to determine the upcoming 5-month production schedule for video recorders. Past production records indicate that 2,000 recorders can be produced per month. An additional 600 recorders can be produced monthly on an overtime basis. Unit cost is $10 for recorders produced during regular working hours and $15 for those produced on an overtime basis. Contracted sales per month are as follows:
Month Contracted Sales (units)
1 1200
2 2100
3 2400
4 3000
5 4000
Inventory carrying costs are $2 per recorder per month. The manager does not want any inventory carried over past the fifth month. The manager wants to know the monthly production that will minimize total production and inventory costs. a. Formulate a linear programming model for this problem. b. Solve the model by using the computer.
Explanation / Answer
I_i = Inventory at end of month I where I = 1234
R1
<=
2000
O1
<=
600
I_1
R2
<=
2000
O2
<=
600
I_2
R3
<=
2000
O3
<=
600
I_3
R4
<=
2000
O4
<=
600
I_4
R5
<=
2000
O5
<=
600
Month
1
=
1200
2
=
2100
3
=
2400
4
=
3000
5
=
4000
I_i = Inventory at end of month I where I = 1234
R1
<=
2000
O1
<=
600
I_1
R2
<=
2000
O2
<=
600
I_2
R3
<=
2000
O3
<=
600
I_3
R4
<=
2000
O4
<=
600
I_4
R5
<=
2000
O5
<=
600
Month
1
=
1200
2
=
2100
3
=
2400
4
=
3000
5
=
4000
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