9 A factory makes three different types of widget: plain, bland and ordinary. Each widget is made using three different machines: \(A , B\) and \(C\). Each plain widget needs 5 minutes on machine \(A , 12\) minutes on machine \(B\) and 24 minutes on machine \(C\). Each bland widget needs 4 minutes on machine \(A , 8\) minutes on machine \(B\) and 12 minutes on machine \(C\). Each ordinary widget needs 3 minutes on machine \(A\), 10 minutes on machine \(B\) and 18 minutes on machine \(C\). Machine \(A\) is available for 3 hours a day, machine \(B\) for 4 hours a day and machine \(C\) for 9 hours a day. The factory must make:
more plain widgets than bland widgets;
more bland widgets than ordinary widgets.
At least \(40 \%\) of the total production must be plain widgets.
Each day, the factory makes \(x\) plain, \(y\) bland and \(z\) ordinary widgets.
Formulate the above situation as 6 inequalities, in addition to \(x \geqslant 0 , y \geqslant 0\) and \(z \geqslant 0\), writing your answers with simplified integer coefficients.
(8 marks)