A realtor is developing a rental housing and retail area. The housing area consists of 3 types of housing: 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 (and there is no need to build more houses than the demand), but the number of duplexes must equal at least 50% of the total number of efficiency apartments and single-family homes. For each efficiency, duplex and single-family apartment, there must be retail space of at least 10 ft^2, 15 ft^2 and 18 ft^2 respectively. However, land availability limits retail space to no more than 10,000 ft^2. The monthly rental income is estimated at $600, $750, and $1200 for efficiency, duplex and single family units respectively. The retail space rents for $100/ft^2. Formulate an LP that would find the amount of retail spare area and number of family residences to maximize rent income.