6 [Figure 3, printed on the insert, is provided for use in this question.]\\
Ernesto is to plant a garden with two types of tree: palms and conifers.\\
He is to plant at least 10, but not more than 80 palms.\\
He is to plant at least 5 , but not more than 40 conifers.\\
He cannot plant more than 100 trees in total.

Each palm needs 20 litres of water each day and each conifer needs 60 litres of water each day. There are 3000 litres of water available each day.

Ernesto makes a profit of $\pounds 2$ on each palm and $\pounds 1$ on each conifer that he plants and he wishes to maximise his profit.

Ernesto plants $x$ palms and $y$ conifers.
\begin{enumerate}[label=(\alph*)]
\item Formulate Ernesto's situation as a linear programming problem.
\item On Figure 3, draw a suitable diagram to enable the problem to be solved graphically, indicating the feasible region and the direction of the objective line.
\item Find the maximum profit for Ernesto.
\item Ernesto introduces a new pricing structure in which he makes a profit of $\pounds 1$ on each palm and $\pounds 4$ on each conifer.

Find Ernesto's new maximum profit and the number of each type of tree that he should plant to obtain this maximum profit.
\end{enumerate}

\hfill \mbox{\textit{AQA D1 2006 Q6 [18]}}