A developer wishes divide a property into lots. To access the lots, the developer must build a road which costs $3000 per foot to build, and will place lots on both sides of the road. They will also need to lay pipes which cost $1000 per foot from the road to the middle of each lot. They have $100 000 to spend on development per lot 

(a) If a lot has width y and length x, find the cost of developing the lot in term of x and y. 

(b) Using the cost of $100 000 find a formula for the width of the lot in terms of the length.

 (c) Find the length and width of the lot which will produce maximum area.