A realtor is developing a rental housing and retail area. The housing areaconsists of efficiency apartments, duplexes, and single-family homes. Maximumdemand by potential renters is estimated to be...

A realtor is developing a rental housing and retail area. The housing areaconsists of efficiency apartments, duplexes, and single-family homes. Maximumdemand by potential renters is estimated to be 500 efficiency apartments, 300duplexes, and 250 single-family homes, but the number of duplexes must equalat least 50% of the number of efficiency apartments and single homes. Retailspace is proportionate to the number of home units at the rates of at least 10ft2,15ft2, and 18ft2 for efficiency, duplex, and single family units, respectively.However, land availability limits retail space to no more than 10,000ft2. Themonthly rental income is estimated at $600, $750, and $1200 for efficiency,duplex, and single-family units, respectively. The retail space rents for $100/ft2.Determine the optimal retail space area and the number of family residences.