CASE STUDY. Linear programming case.
A car manufacturing company has defined its demand for three of its best-selling units. The following table shows the information for the next three years:
|
Año
|
Tipo 1
|
Tipo 2
|
Tipo 3
|
|
1
|
180
|
210
|
160
|
|
2
|
240
|
160
|
180
|
|
3
|
220
|
140
|
150
|
This implies that in the first year a maximum of 180 units of type 1 can be sold,210 units of type 2, and 160 units of type 3. Each type 1 unit is sold at $180,000 and it costs $145,000 dollars for unit to produce. Type 2 unitssell at $210,000, witha manufacturing cost of$170,200. Finally, the manufacturing cost of the type 3 unit is $130,000 while its selling price is $160,000. The manufacturing conditions of the supplying plants make it possible to produce up to 475 units per year regardless of the type of car in question.
On the other hand, the company has a store where they can accumulate units to be used in another time period. The storage cost of one unit is 20,000 per year.Likewise, the company has sustainability programs and has therefore established rigorous anti-pollution programs. One is that vehicles manufactured each year must not exceed an average of 10 units of pollution.According to the specifications of each vehicle, it is known that each type 1 vehicle generates 5 units of pollutants, each type 2 generates 15 units and each type 3 generates 10 units of pollutants. As production system manager you are asked to answer the following question to the senior management.
How many units of each type must produce per year to obtain the maximum utility?