4 An eco-village is to be constructed consisting of large houses and standard houses.
Each large house has 4 bedrooms, needs a plot size of \(200 \mathrm {~m} ^ { 2 }\) and costs \(\pounds 60000\) to build.
Each standard house has 3 bedrooms, needs a plot size of \(120 \mathrm {~m} ^ { 2 }\) and costs \(\pounds 50000\) to build.
The area of land available for houses is \(120000 \mathrm {~m} ^ { 2 }\). The project has been allocated a construction budget of \(\pounds 42.4\) million. The market will not sustain more than half as many large houses as standard houses. So, for instance, if there are 500 standard houses then there must be no more than 250 large houses.

1. Define two variables so that the three constraints can be formulated in terms of your variables. Formulate the three constraints in terms of your variables.
2. Graph your three inequalities from part (i), indicating the feasible region.
3. Find the maximum number of bedrooms which can be provided, and the corresponding numbers of each type of house.
4. Modify your solution if the construction budget is increased to \(\pounds 45\) million.