7 An engineering company makes brake kits and clutch kits to sell to motorsport teams.

The table below summarises the time taken and costs involved in making the two different types of kit.

\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
Type of kit & Time taken to make a kit (hours) & Cost to engineering company per kit (£) & Profit to engineering company per kit (£) \\
\hline
Brake kit & 5 & 500 & 2000 \\
\hline
Clutch kit & 3 & 200 & 1000 \\
\hline
\end{tabular}
\end{center}

The workers at the engineering company have a combined 2500 hours available to make the kits every month.

The engineering company has $\pounds 200000$ available to cover the costs of making the kits every month.

To meet the minimum demands of the motorsport teams, the engineering company must make at least 100 of each type of kit every month.

7
\begin{enumerate}[label=(\alph*)]
\item Using a graphical method on the grid opposite, find the number of each type of kit that the engineering company should make every month, in order to maximise its total monthly profit.

Show clearly how you obtain your answer.\\

\includegraphics[max width=\textwidth, alt={}, center]{c297a67f-65fd-47e0-a60c-d38fd86c6081-13_2486_1709_221_153}

Do not write outside the box

7
\item Give a reason why the engineering company may not be able to make the number of each kit that you found in part (a).

7
\item During one particular month the engineering company removes the need to make at least 100 of each type of kit.

Explain whether or not this has an effect on your answer to part (a).
\end{enumerate}

\hfill \mbox{\textit{AQA Further Paper 3 Discrete 2020 Q7 [11]}}