Management Science Linear Programming Housing Development Case Background Carter is a real estate firm located in the Columbia, SC metropolitan area that specializes in residential real estate. Carter has $2 million available for the purchase of new rental property After an initial screening, Carter reduced the investment alternatives to townhouses and apartment buildings. Each townhouse can be purchased for $282,000 and five are available. Each apartment building can be purchased for $400,000, and the developer will construct as many buildings as Carter wants to purchase. Carter's property manager can devote up to 140 hours per month to these new properties; each townhouse is expected to require 4 hours per month, and each apartment building is expected to require 40 hours per month. The annual cash flow, after deducting mortgage payments and operating expenses, is estimated to be $10,000 per townhouse and $15,000 per apartment building. Carters ownership group would like determine the number of townhouses and the number of apartment buildings to purchase to maximize annual cash flow. Analysis Given that. T=number of townhouses to purchase; and A = number of apartment buildings to purchase, provide a linear programming analysis of the following What is the the number of townhouses and apartment buildings that Carter Realty has to purchase to maximize its annual cash flow? 1 What is the major problem with the results of this analysis? What does Carter Realty need to do to solve the problem? What secondary problems are created by solving this problem think in terms of the constraints)