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There are \(50\) boxes in a factory. The weights, \(w\) in \(kg\), are divided into \(5\) classes, as shown in the table below.

1. Show that the estimated mean weight of the boxes is \(32\,kg\).

2. In the factory, there are \(x\) boxes labelled "Fragile". They are all in class \(E\). The estimated mean weight of all the other boxes in the factory is \(30\,kg\).

   Calculate the value of \(x\).

3. A delivery of \(y\) additional boxes, all with a weight in class \(D\), is brought to the factory.

   The total estimated mean weight of all the boxes in the factory is less than \(33\,kg\).

   Find the largest possible value of \(y\).