7. A linear programming problem is modelled by the following constraints
$$\begin{aligned}
8 x + 3 y & \leqslant 480
8 x + 7 y & \geqslant 560
y & \geqslant 4 x
x , y & \geqslant 0
\end{aligned}$$
- Use the grid provided in your answer book to represent these inequalities graphically. Hence determine the feasible region and label it R .
The objective function, \(F\), is given by
$$F = 3 x + y$$
- Making your method clear, determine
- the minimum value of the function \(F\) and the coordinates of the optimal point,
- the maximum value of the function \(F\) and the coordinates of the optimal point.