To grow a certain vegetable crop, a farmer needs to ensure that there is a sufficient concentration of the macro-nutrients nitrogen, phosphorus and potassium in her soil. To achieve this she will apply two types of fertiliser to her soil, Fertiliser 1 and Fertiliser 2. She needs to have at least 36 units of nitrogen, at least 20 units of phosphorus and no more than 28 units of potassium present in the fertiliser that she applies to her soil. The composition of macro-nutrients in each of the two types of fertilisers is described in the following table.
Fertiliser 1 Fertiliser 2
Nitrogen (units/kg) 9 2
Phosphorus (units/kg) 2 6
Potassium (units/kg) 4 5
Fertiliser 1 costs $20/kg while Fertiliser 2 costs $15/kg. The farmer wants to know how many bags of each type of fertiliser should be used to minimise the cost.
Formulate the problem above as an optimisation problem, don't solve it.