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- #1

Particularly equation [3]. Thank you.

...................................................................................

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:

Code:

```
Grade %Phosphorus %Ash $/Tonne
a 1 0.03 3 80
b 2 0.05 14 60
c 3 0.08 8 90
```

by the following Linear Programming problem.

Find a, b, c to minimize Z = 80a + 60b + 90c subject to:

3a + 5b + 8c ≤ 4 [1]

3a +14b + 8c ≤ 5 [2]

a + b + c ≤ 1 [3]

Non-negativity constraint = a, b, c ≥ 0.

Take care in your answer to define the decision variables and to explain briefly

how the objective funtions and the constraints are derived