## Linear Programming Problem

Need help to solve Linear Programming problem.

President of a Real Estate Co. is building houses on 800 acres. Single, double and triple family houses will be built. 15% of the land will be used for roads. The company expect profits of $10,000 - Single Unit,$12,000 - Double Unit and $15,000 - Triple Unit. Cost associated with providing water services and the amount of water consumed is stated below. Unit Type Single Double Triple Recreation Area Water Serv. Cost/Unit($) 1,000 1,200 1,400 800_____

Water Consum
per Unit(gals) 400 600 840 450

Contraints
The Real Estate Co. must collect at least \$100,000 for the water servies project to be economically feasible. Water supply capacity is limited to
200, 000 in total.
Also, only single, double & triple family houses can be built of which single units must be at least 50% of the total houses built. Minimum lot sizes of 2, 3, & 4 acres are required for single, double & triple units respectively. Finally, recreational areas of 1 acre each must be eastablished at a rate of one per 200 families.

Question:
Formulate the necessary inequalities to solve the problem.
i.e. Objective Function and other inequalities related to the constraints.