The city of Fayetteville is embarking on an urban renewal project that will include lowerand middle-income row housing, upper-income luxury apartments, and public housing. The project also includes a public elementary school and retail facilities. The size of the elementary school (number of classrooms) is proportional to the number of pupils, and the retail space is proportional to the number of housing units. The following table provides the pertinent data of the situation:

The new school can occupy a maximum space of 2 acres at the rate of at most 25 pupils per room. The operating annual cost per schoolroom is $10,000. The project will be located on a 50-acre vacant property owned by the city. Additionally, the project can make use of an adjacent property occupied by 200 condemned homes. Each condemned home occupies .25 acre. The cost of buying and demolishing a condemned unit is $7000. Open space, streets, and parking lots consume 15% of total available land. Develop an LP to determine the optimum plan for the project, and find the solution using AMPL, Solver, or TORA.

Transcribed Image Text:

Minimum number of units Maximum number of units Lot size per unit (acre) Average number of pupils per unit Retail demand per unit (acre) Annual income per unit ($) Lower income 100 200 .05 1.3 .023 7000 Middle income 125 190 .07 1.2 .034 12,000 Upper Public School Retail income housing room unit 75 260 .03 .5 .046 20,000 300 600 .025 1.4 .023 5000 .045 .034 - 0 25 .1 15,000