Realco owns 900 acres of undeveloped land on a scenic lake in the heart of the Ozark Mountains. In the past, little or no regulation was imposed upon new developments around the lake. The lake shores are now dotted with vacation homes, and septic tanks are in extensive use, most of them improperly installed. Over the years, seepage from the septic tanks led to severe water pollution. To curb further degradation of the lake, county officials have approved stringent ordinances applicable to all future developments:

(1) Only single-, double-, and triple-family homes can be constructed, with single-family homes accounting for at least 50% of the total. (2) To limit the number of septic tanks, minimum lot sizes of 2, 3, and 5 acres are required for single-, double-, and triple-family homes, respectively. (3) Recreation areas of 1 acre each must be established at the rate of one area per 220 families. (4) To preserve the ecology of the lake, underground water may not be pumped out for house or garden use. The president of Realco is studying the possibility of developing the 800-acre property. The new development will include single-, double-, and triple-family homes. It is estimated that 15% of the acreage will be allocated to streets and utility easements. Realco estimates the returns from the different housing units as follows:

Housing unit Single Double Triple Net return per unit ($) 12,000 15,000 18,000 The cost of connecting water service to the area is proportionate to the number of units constructed. However, the county charges a minimum of $120,000 for the project.

Additionally, the expansion of the water system beyond its present capacity is limited to 220,000 gallons per day during peak periods. The following data summarize the water service connection cost as well as the water consumption, assuming an average size family:

Housing unit Single Double Triple Recreation Water service connection cost per unit ($) 1000 1200 1400 800 Water consumption per unit (gal/day) 400 600 840 450 Develop an LP model to determine the optimal plan for Realco, and find the solution using AMPL, Solver, or TORA.