8 [Figure 2, printed on the insert, is provided for use in this question.]\\
A company makes two types of boxes of chocolates, executive and luxury.\\
Every hour the company must make at least 15 of each type and at least 35 in total.\\
Each executive box contains 20 dark chocolates and 12 milky chocolates.\\
Each luxury box contains 10 dark chocolates and 18 milky chocolates.\\
Every hour the company has 600 dark chocolates and 600 milky chocolates available.\\
The company makes a profit of $\pounds 1.50$ on each executive box and $\pounds 1$ on each luxury box.\\
The company makes and sells $x$ executive boxes and $y$ luxury boxes every hour.\\
The company wishes to maximise its hourly profit, $\pounds P$.
\begin{enumerate}[label=(\alph*)]
\item Show that one of the constraints leads to the inequality $2 x + 3 y \leqslant 100$.
\item Formulate the company's situation as a linear programming problem.
\item On Figure 2, draw a suitable diagram to enable the problem to be solved graphically, indicating the feasible region and an objective line.
\item Use your diagram to find the maximum hourly profit.
\end{enumerate}

\hfill \mbox{\textit{AQA D1 2005 Q8 [13]}}