7. Becky's bird food company makes two types of bird food. One type is for bird feeders and the other for bird tables. Let \(x\) represent the quantity of food made for bird feeders and \(y\) represent the quantity of food made for bird tables. Due to restrictions in the production process, and known demand, the following constraints apply.
$$\begin{gathered}
x + y \leq 12
y < 2 x
2 y \geq 7
y + 3 x \geq 15
\end{gathered}$$
- On the axes provided, show these constraints and label the feasible region \(R\).
The objective is to minimise \(C = 2 x + 5 y\).
- Solve this problem, making your method clear. Give, as fractions, the value of \(C\) and the amount of each type of food that should be produced.
(4)
Another objective (for the same constraints given above) is to maximise \(P = 3 x + 2 y\), where the variables must take integer values. - Solve this problem, making your method clear. State the value of \(P\) and the amount of each type of food that should be produced.