4 A wall 4 metres long and 3 metres high is to be tiled. Two sizes of tile are available, 10 cm by 10 cm and 30 cm by 30 cm .
- If \(x\) is the number of boxes of ten small tiles used, and \(y\) is the number of large tiles used, explain why \(10 x + 9 y \geqslant 1200\).
There are only 100 of the large tiles available.
The tiler advises that the area tiled with the small tiles should not exceed the area tiled with the large tiles. - Express these two constraints in terms of \(x\) and \(y\).
The smaller tiles cost 15 p each and the larger tiles cost \(\pounds 2\) each.
- Given that the objective is to minimise the cost of tiling the wall, state the objective function. Use the graphical approach to solve the problem.
- Give two other factors which would have to be taken into account in deciding how many of each tile to purchase.