7. You are in charge of buying new cupboards for a school laboratory. The cupboards are available in two different sizes, standard and large.
The maximum budget available is \(\pounds 1800\). Standard cupboards cost \(\pounds 150\) and large cupboards cost \(\pounds 300\).
Let \(x\) be the number of standard cupboards and \(y\) be the number of large cupboards.

1. Write down an inequality, in terms of \(x\) and \(y\), to model this constraint.
   (2) The cupboards will be fitted along a wall 9 m long. Standard cupboards are 90 cm long and large cupboards are 120 cm long.
2. Show that this constraint can be modelled by $$3 x + 4 y \leqslant 30$$ You must make your reasoning clear. Given also that \(y \geqslant 2\),
3. explain what this constraint means in the context of the question. The capacity of a large cupboard is \(40 \%\) greater than the capacity of a standard cupboard. You wish to maximise the total capacity.
4. Show that your objective can be expressed as $$\text { maximise } 5 x + 7 y$$
5. Represent your inequalities graphically, on the axes in your answer booklet, indicating clearly the feasible region, R.
6. Find the number of standard cupboards and large cupboards that need to be purchased. Make your method clear.