Example $2\mathrm{.}4-6($Urban Renewal Model$)$The city of Erstville is faced with a severe budget shortage. Seeking a long$-$term solution, the city council votes to improve the tax base by condemning an inner$-$city housing area and replacing it with a modern development.The project involves two phases: $(1)$ demolishing substandard houses to provide land for the new development and $(2)$ building the new development. The following is a summary of the situation$\mathrm{.}1.$ As many as $300$ substandard houses can be demolished. Each house occupies a $\mathrm{.}25-$acre lot.The cost of demolishing a condemned house is $$2000\mathrm{.}2.$ Lot sizes for new single$-,$ double$-,$ triple$-,$ and quadruple$-$family homes $($units$)$ are $\mathrm{.}18,\mathrm{.}28,\mathrm{.}4,$ and $\mathrm{.}5$ acre, respectively. Streets, open space, and utility easements account for $15\%$ of available acreage$\mathrm{.}3.$ In the new development, the triple and quadruple units account for at least $25\%$ of the total. Single units must be at least $20\%$ of all units, and double units at least $10\%.$Al The tax levied per unit for single, double, triple, and quadruple units is $$1000,$ $$1900,$ $$2700,$and $$3400,$ respectively$\mathrm{.}5.$ The construction cost per unit for single$-,$ double$-,$ triple$-,$ and quadruple$-$family homes is $$50,000,$ $$70,000,$ $$130,000,$ and $$160,000,$ respectively$\mathrm{.}6.$ Financing through a local bank is limited to $$15$ million.How many units of each type should be constructed to maximize tax collection?