How to optimize your production
We would like to produce trousers, skirts, and jackets in our workshop. We have three kind of raw material: textile (800 metres), buttons (2600 pieces) and thread (1400 rolls). We can sell the finished products with the following prices: 40 € (in case of trousers), 30 € (skirt) and 90 € (jacket). What amount should we fabricate from the above products in order to maximize income?
The requisites are listed in the table:
| Trousers (x) | Skirt (y) | Jacket (z) | Stock | |
| Textil | 1,2 | 0,8 | 2,4 | 800 meters |
| Button | 4 | 2 | 7 | 2600 pieces |
| Thread | 2 | 1 | 4 | 1400 rolls |
| Selling rate | 40 | 30 | 90 | maximum? |
1. We can make a mathematical model:
| Model | ||
| Textile | 1.2 x + 0.8 y + 2.4 z ≤ 800 | |
| Button | 4.0 x + 2.0 y + 7.0 z ≤ 2600 | |
| Thread | 2.0 x + 1.0 y + 4.0 z ≤ 1400 | |
| Profit | 40 x + 30 y + 90 z → max | |
2. Open EuroOffice Calc (or OpenOffice.org Calc). Make the next table:
The cells with yellow background
contain arbitrary initial values for the EuroOffice Solver.
3. Choose an optimization method for EuroOffice Solver in the Tools menu. Choose the Simplex method.
4. At first you can choose between Maximize and Minimize. Choose the Maximize, because we would like to maximize our profit.
5. Select the Target coefficients
6. Select the Variable range.
7. Select the Constraint range.
8. At the end you can choose between 'Solve just once' and 'Solve continously'. The first one solve just this problem, the second one gives chance to adjust the earlier set parameter, and the solution is updated automatically.
9. The solution can be read in the yellow cells, which were marked as 'Variable range'.
Now one can see that we have to produce just skirts.
