A firm selling cooking coal to power stations, requires to formulate a blend of coal with a phosphorus content of at most 0.04% and ash impurity of at most 5%. Three different grades of coal are available to blend; the phosphorus and ash content and the price of each grade are given in the table below:
Question: Show that the problem of determining the optimal blend can be modelled by the followingLinear Programming problem. Find X1, X2, X3 is in R (real) to minimize Z= 8X1 + 6X2 + 9X3 subject to:
Non-negativity constraint = X1, X2, X3 ≥ 0.
Take care in your answer to define the decision variables and to explain briefly how the objective funtions and the constraints are derived.
Grade | % Phosphorus | % Ash | $/Tonne |
1 | 0.03 | 3 | 80 |
2 | 0.05 | 14 | 60 |
3 | 0.08 | 8 | 90 |
- 3X1+ 5X2+ 8X3 ≤ 4
- 3X1+14X2+ 8X3 ≤ 5
- X1+ X2+ X3 ≤ 1
Non-negativity constraint = X1, X2, X3 ≥ 0.
Take care in your answer to define the decision variables and to explain briefly how the objective funtions and the constraints are derived.