8 Each day, a factory makes three types of hinge: basic, standard and luxury. The hinges produced need three different components: type \(A\), type \(B\) and type \(C\). Basic hinges need 2 components of type \(A , 3\) components of type \(B\) and 1 component of type \(C\). Standard hinges need 4 components of type \(A , 2\) components of type \(B\) and 3 components of type \(C\). Luxury hinges need 3 components of type \(A\), 4 components of type \(B\) and 5 components of type \(C\). Each day, there are 360 components of type \(A\) available, 270 of type \(B\) and 450 of type \(C\). Each day, the factory must use at least 720 components in total.
Each day, the factory must use at least \(40 \%\) of the total components as type \(A\).
Each day, the factory makes \(x\) basic hinges, \(y\) standard hinges and \(z\) luxury hinges.
In addition to \(x \geqslant 0 , y \geqslant 0 , z \geqslant 0\), find five inequalities, each involving \(x , y\) and \(z\), which must be satisfied. Simplify each inequality where possible.