1. (25 points) Urban renewal has come to the Southeast neighborhood in the city of Bal-...

Transcribed Image Text:

1. (25 points) Urban renewal has come to the Southeast neighborhood in the city of Bal- ington. The renewal project is a mix of housing, a new public school, and retail facilities. The housing is divided into four types: public housing, lower- and middle-income brown- stones, and luxury condos. The new school can occupy a maximum space of 2.5 acres at a rate of at most 22 students per room. The annual operating cost per schoolroom is $12,000. Additional information about the project is provided in the following table. Public Lower Middle Luxury School Retail Housing Income Income Condos Room Unit Minimum units Maximum units 300 100 125 75 0 600 200 240 225 25 Lot size per unit (acres) 0.025 0.05 0.10 0.04 0.045 0.1 Average students per unit 1.8 1.4 1.3 0.6 Retail demand per unit (acres) 0.023 0.023 0.034 0.046 0.034 Annual income per unit ($) 5000 7000 12000 25000 15000 The city has obtained a 50-acre vacant property for this project and may also purchase space from an adjacent property on which there are currently 500 condemned houses. Each condemned house is on a lot of 0.25 acres. The cost of buying and demolishing a condemned house is $7000. To enhance the appeal of the redesigned neighborhood, open space must equal at least 20% of the total land available for redevelopment. Formulate a linear program to help Balington to meet the stated constraints and minimize the total costs associated with the Southeast neighborhood redevelopment. Do NOT use a generic model. Make sure to define all variables and label all functional constraints. 1. (25 points) Urban renewal has come to the Southeast neighborhood in the city of Bal- ington. The renewal project is a mix of housing, a new public school, and retail facilities. The housing is divided into four types: public housing, lower- and middle-income brown- stones, and luxury condos. The new school can occupy a maximum space of 2.5 acres at a rate of at most 22 students per room. The annual operating cost per schoolroom is $12,000. Additional information about the project is provided in the following table. Public Lower Middle Luxury School Retail Housing Income Income Condos Room Unit Minimum units Maximum units 300 100 125 75 0 600 200 240 225 25 Lot size per unit (acres) 0.025 0.05 0.10 0.04 0.045 0.1 Average students per unit 1.8 1.4 1.3 0.6 Retail demand per unit (acres) 0.023 0.023 0.034 0.046 0.034 Annual income per unit ($) 5000 7000 12000 25000 15000 The city has obtained a 50-acre vacant property for this project and may also purchase space from an adjacent property on which there are currently 500 condemned houses. Each condemned house is on a lot of 0.25 acres. The cost of buying and demolishing a condemned house is $7000. To enhance the appeal of the redesigned neighborhood, open space must equal at least 20% of the total land available for redevelopment. Formulate a linear program to help Balington to meet the stated constraints and minimize the total costs associated with the Southeast neighborhood redevelopment. Do NOT use a generic model. Make sure to define all variables and label all functional constraints.