5. A school awards two types of prize, junior and senior. The school decides that it will award at least 25 junior prizes and at most 60 senior prizes.
Let \(x\) be the number of junior prizes that the school awards and let \(y\) be the number of senior prizes that the school awards.

1. Write down two inequalities to model these constraints.
   (2) Two further constraints are $$\begin{aligned} & 2 x + 5 y \geqslant 250
   & 5 x - 3 y \leqslant 150 \end{aligned}$$
2. Add lines and shading to Diagram 1 in the answer book to represent all four of these constraints. Hence determine the feasible region and label it \(R\). The cost of a senior prize is three times the cost of a junior prize. The school wishes to minimise the cost of the prizes.
3. State the objective function, giving your answer in terms of \(x\) and \(y\).
4. Determine the exact coordinates of the vertices of the feasible region. Hence use the vertex method to find the number of junior prizes and the number of senior prizes that the school should award. You should make your working clear.