7 Sam is making pies.
There is exactly enough pastry to make 7 large pies or 20 medium pies or 36 small pies, or some mixture of large, medium and small pies. This is represented as a constraint \(180 x + 63 y + 35 z \leqslant 1260\).

1. Write down what \(\mathrm { X } , \mathrm { Y }\) and Z represent. There is exactly enough filling to make 5 large pies or 12 medium pies or 18 small pies, or some mixture of large, medium and small pies.
2. Express this as a constraint of the form \(a x + b y + c z \leqslant d\), where \(a , b , c\) and \(d\) are integers. The number of small pies must equal the total number of large and medium pies.
3. Show that making exactly 9 small pies is inconsistent with the constraints.
4. Determine the maximum number of large pies that can be made.
   • Your reasoning should be in the form of words, calculations or algebra.
   • You must check that your solution is feasible.