Math 540 - Quantitative MAth
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 4 5 |
2400 3000 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.
c) Answer all highlighter sections
|
Videotechnics Company (Multi Production and Inventory) | ||||||||||||
|
Let Ri = Regular production in month I, where I = 1,2,3,4,5 |
Cost for recorders produced during regular working hours is $10 | |||||||||||
|
Oi = Overtime production in month I, where I = 1,2,3,4,5 |
Cost for recorders produced during regular working hours is $15 | |||||||||||
|
I_i = Inventory at end of month I, where I = 1,2,3,4 | ||||||||||||
|
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 | ||||||||||
|
Objective function | ||||||||||||
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