6. 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 30 p on each Badge 1 sold and 40 p 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 .

1. Formulate this situation as a linear programming problem, simplifying your inequalities so that all the coefficients are integers.
2. On the grid provided in the answer book, construct and clearly label the feasible region.
3. Using your graph, advise the company on the number of each badge it should produce. State the maximum profit "Decide" will make.
   (3)