The Young Enterprise Company "Decide", is going to produce badges to sell to decision maths students. It will produce two types of badges.

Badge 1 reads "I made the decision to do maths" and
Badge 2 reads "Maths is the right decision".

"Decide" must produce at least 200 badges and has enough material for 500 badges.

Market research suggests that the number produced of Badge 1 should be between 20% and 40% of the total number of badges made.

The company makes a profit of 30p on each Badge 1 sold and 40p on each Badge 2. It will sell all that it produced, and wishes to maximise its profit.

Let $x$ be the number produced of Badge 1 and $y$ be the number of Badge 2.

\begin{enumerate}[label=(\alph*)]
\item Formulate this situation as a linear programming problem, simplifying your inequalities so that all the coefficients are integers. [6]

\item On the grid provided in the answer book, construct and clearly label the feasible region. [5]

\item Using your graph, advise the company on the number of each badge it should produce. State the maximum profit "Decide" will make. [3]
\end{enumerate}

\hfill \mbox{\textit{Edexcel D1 2004 Q6 [14]}}