QUESTION # 2 (20 points): Madrid is facing an urban planning issue in which many illegal houses are constructed on encroached land. Local council has come to agreement with occupants of these houses in which it will pay them compensation and they will vacate these houses. After these houses are vacated, they will be abolished and replaced with modern development which will also help in increasing tax revenue. The city council is evaluating whether it should go ahead with this project and thus wants to know the maximum amount of tax revenue they can generate from this project. This project involves two phases. First demolition of illegal construction to provide land for new development and second phase include the new development itself. The following data provides the description of this project. 1. A total of 300 illegal houses will be demolished. Each house occupies a 0.25-acre lot. The cost of demolishing is $ 2,000. 2. Lot size of new single, double, triple and quadruple family homes are 0.18, 0.28, 0.4 and 0.5 acre respectively. Street, 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% od the total. Single units must be at least 20% of all units and double units at least 10%. 4. The tax levied per unit for single, double, triple, and quadruple family homes 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, S 130,000 and $ 160,000 respectively. Maximum financing available from the bank for this project is $ 15 million. Construct a mathematical model which maximize tax revenue ? Under what condition should city government go ahead with this project. QUESTION # 2 (20 points): Madrid is facing an urban planning issue in which many illegal houses are constructed on encroached land. Local council has come to agreement with occupants of these houses in which it will pay them compensation and they will vacate these houses. After these houses are vacated, they will be abolished and replaced with modern development which will also help in increasing tax revenue. The city council is evaluating whether it should go ahead with this project and thus wants to know the maximum amount of tax revenue they can generate from this project. This project involves two phases. First demolition of illegal construction to provide land for new development and second phase include the new development itself. The following data provides the description of this project. 1. A total of 300 illegal houses will be demolished. Each house occupies a 0.25-acre lot. The cost of demolishing is $ 2,000. 2. Lot size of new single, double, triple and quadruple family homes are 0.18, 0.28, 0.4 and 0.5 acre respectively. Street, 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% od the total. Single units must be at least 20% of all units and double units at least 10%. 4. The tax levied per unit for single, double, triple, and quadruple family homes 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, S 130,000 and $ 160,000 respectively. Maximum financing available from the bank for this project is $ 15 million. Construct a mathematical model which maximize tax revenue ? Under what condition should city government go ahead with this project
