7 A builder needs some screws, nails and plugs. At the local store, there are packs containing a mixture of the three items. A DIY pack contains 200 nails, 200 screws and 100 plugs.
A trade pack contains 1000 nails, 1500 screws and 2500 plugs.
A DIY pack costs \(\pounds 2.50\) and a trade pack costs \(\pounds 15\).
The builder needs at least 5000 nails, 6000 screws and 4000 plugs.
The builder buys \(x\) DIY packs and \(y\) trade packs and wishes to keep his total cost to a minimum.

1. Formulate the builder's situation as a linear programming problem.
2. 1. On the grid opposite, draw a suitable diagram to enable the problem to be solved graphically, indicating the feasible region and the direction of an objective line.
   2. Use your diagram to find the number of each type of pack that the builder should buy in order to minimise his cost.
   3. Find the builder's minimum cost.