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. 1. as many as 300 substandard houses can be demolished. each house occupies a 25-acre lot. the cost of demolishing a condemned house is $2000. 2. lot sizes for new single-, double-, triple-, and quadruple-family homes (units) are .18, .28, a, and.5 acre, respectively. streets, open space, and utility easements account for 15% of available acreage. 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%. 4. tile tax levied per unit for single, double, triple, and quadruple units is $1,000, $1,900, $2,700, and $3,400, respectively. 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. financing through a local bank can amount to a maximum of $15 million.
a) [2 points] define the variables.
b) [12 points] write the mathematical formulation of the problem and state the optimal solution.