5 [Figure 2, printed on the insert, is provided for use in this question.]\\
The Jolly Company sells two types of party pack: excellent and luxury.\\
Each excellent pack has five balloons and each luxury pack has ten balloons.\\
Each excellent pack has 32 sweets and each luxury pack has 8 sweets.\\
The company has 1500 balloons and 4000 sweets available.\\
The company sells at least 50 of each type of pack and at least 140 packs in total.\\
The company sells $x$ excellent packs and $y$ luxury packs.
\begin{enumerate}[label=(\alph*)]
\item Show that the above information can be modelled by the following inequalities.

$$x + 2 y \leqslant 300 , \quad 4 x + y \leqslant 500 , \quad x \geqslant 50 , \quad y \geqslant 50 , \quad x + y \geqslant 140$$

(4 marks)
\item The company sells each excellent pack for 80 p and each luxury pack for $\pounds 1.20$. The company needs to find its minimum and maximum total income.
\begin{enumerate}[label=(\roman*)]
\item On Figure 2, draw a suitable diagram to enable this linear programming problem to be solved graphically, indicating the feasible region and an objective line.
\item Find the company's maximum total income and state the corresponding number of each type of pack that needs to be sold.
\item Find the company's minimum total income and state the corresponding number of each type of pack that needs to be sold.
\end{enumerate}\end{enumerate}

\hfill \mbox{\textit{AQA D1 2007 Q5 [16]}}