A realtor is developing a rental housing and retail area. The housing area consists of efficiency apartments, duplexes, and single-family homes. Maximum demand by potential renters is estimated to be 500 efficiency apartments, 300 duplexes, and 250 single-family homes, but the number of duplexes must equal at least 50% of the number of efficiency apartments and single homes. Retail space is proportionate to the number of home units at the rates of at least 12 ft2, 18 ft2, and 20 ft2 for efficiency, duplex, and single family units, respectively. However, land availability limits retail space to no more than 15,000 ft2.

The monthly rental income is estimated at $650, $800, and $1500 for efficiency-, duplex-, and single-family units, respectively. The retail space rents for $120/ft2. Develop an LP model to determine the optimal retail space area and the number of family residences, and find the solution using AMPL, Solver, or TORA.