A retailer is developing a new rental housing 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. Housing zoning laws will only allow a total of 800 new housing units to be built. The monthly rental income is estimated at $600, $750, and $1200 for efficiency, duplex, and single-family homes respectively. How many efficiency apartments, duplexes, and single-family homes should be constructed to maximize rental income?

a) Define the decision variables.

b) Write the objective function.

c) Write the constraints in standard form.