6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{0360f78d-e18c-4c47-a2ec-ddd705a4175f-7_1214_1581_251_242}
\captionsetup{labelformat=empty}
\caption{Figure 6}
\end{figure}
The graph in Figure 6 is being used to solve a linear programming problem. Two of the constraints have been drawn on the graph and the rejected regions shaded out.
- Write down the constraints shown on the graph.
Two further constraints are
$$\begin{aligned}
x + y & \geqslant 30
\text { and } \quad 5 x + 8 y & \leqslant 400
\end{aligned}$$ - Add two lines and shading to Graph 1 in your answer book to represent these constraints. Hence determine the feasible region and label it R .
The objective is to
$$\text { minimise } 15 x + 10 y$$
- Draw a profit line on Graph 1 and use it to find the optimal solution. You must label your profit line clearly.
(3)