Math Problem Solver

Write the mathematical model for the following situation. 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:

(i) 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 $.(ii) Lot sizes for new single, double, triple, and quadruple-family homes (units) are .18, .28,.4, and .5 acre, respectively. Streets, open space, and utility easements account for 15% ofavailable acreage.(iii) In the new development the triple and quadruple units account for at least 25% of thetotal. Single units must be at least 20% of all units and double units at least 10%.(iv) The tax levied per unit for single, double, triple, and quadruple units is 1,000$, 1,900$,2,700$, and 3,400$, respectively.(v) The construction cost per unit for single-, double, triple, and quadruple-family homes is50,000$, 70,000$, 130,000$, and 160,000$, respectively. Financing through a local bank canamount to a maximum of 15 million$.