Question

A fruit grower can use two types of fertilizer in his garden, brand P and brand Q. Tests indicate that the garden needs at least 240 kg of phosphoric acid, at least 270 kg of potash and at most 310 kg of chlorine. The amounts (in kg) of nitrogen, phosphoric acid, potash, and chlorine in a bag of each brand are given in the table below. If the grower wants to minimise the amount of nitrogen added to the garden, how many bags of each brand should be used? What is the minimum amount of nitrogen added in the garden? \[\] $\begin{matrix} \text{kg per bag:}& \text{Brand P} &\text{Brand Q} \\ \text {Nitrogen} &3 & 3.5\\ \text {Phosphoric Acid}& 1 & 2\\ \text {Potash}&3 &1.5 \\ \text {Chlorine}& 1.5 & 2 \end{matrix}$