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Question: a realtor is developing a rental housing and retail area...

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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 ft2, 15 ft2 and 18 ft2 respectively. However, land availability limits retail space to no more than 10,000 ft2. 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/ft2. Formulate an LP that would find the amount of retail space area and number of family residences to maximize rent income.

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