A realtor is developing 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 10 ft, 15 ft and 18 ft for efficiency, duplex and single family units, respectively. However the land availability limits retail space to no more than 10,000ft. The monthly rental income is estimated at $600, $750, and $1200 for efficiency, duplex and single family units respectively. The reatil space rents for $100ft. Develop a Linear Programing model to determine the optimal retail space area and the number of family residences.