The production manager of Videotechnics Company is attemptin

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.

Solution

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