7 A factory makes batches of three different types of battery: basic, long-life and super.
Each basic batch needs 4 minutes on machine \(A\), 7 minutes on machine \(B\) and 14 minutes on machine \(C\). Each long-life batch needs 10 minutes on machine \(A\), 14 minutes on machine \(B\) and 21 minutes on machine \(C\). Each super batch needs 10 minutes on machine \(A\), 14 minutes on machine \(B\) and 28 minutes on machine \(C\). Machine \(A\) is available for 4 hours a day, machine \(B\) for 3.5 hours a day and machine \(C\) for 7 hours a day. Each day the factory must make:
more basic batches than the total number of long-life and super batches; at least as many long-life batches as super batches. At least 15\% of the production must be long-life batches.
Each day, the factory makes \(x\) basic, \(y\) long-life and \(z\) super batches.
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.

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7 A factory makes batches of three different types of battery: basic, long-life and super.\\
Each basic batch needs 4 minutes on machine $A$, 7 minutes on machine $B$ and 14 minutes on machine $C$.

Each long-life batch needs 10 minutes on machine $A$, 14 minutes on machine $B$ and 21 minutes on machine $C$.

Each super batch needs 10 minutes on machine $A$, 14 minutes on machine $B$ and 28 minutes on machine $C$.

Machine $A$ is available for 4 hours a day, machine $B$ for 3.5 hours a day and machine $C$ for 7 hours a day.

Each day the factory must make:\\
more basic batches than the total number of long-life and super batches; at least as many long-life batches as super batches.

At least 15\% of the production must be long-life batches.\\
Each day, the factory makes $x$ basic, $y$ long-life and $z$ super batches.\\
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.

\hfill \mbox{\textit{AQA D1 2014 Q7 [8]}}