TOK is working on a housing project to maximize the collected tax. The project involves two phases: (l) demolishing substandard houses and (2) building the new houses. The following is a summary of the situation. The number of substandard houses that can be demolished is at most 300. Each house occupies a 0.25-acre lot. The cost of demolishing a condemned house is 2000TL. Lot sizes for new single-, double-, triple-, and quadruple-family homes (units) are 0.18, 0.28, 0.4, and 0.5 acres, respectively. Streets, open space, and utility easements account for 15% of available acreage. 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%. The tax to be collected per unit for single, double, triple, and quadruple units is 1,000TL, 1,900TL, 2,700TL, and 3,400TL, respectively. The construction cost per unit for single-, double-, triple-, and quadruple- family homes is 50,000TL, 70,000TL, 130,000TL, and 160,000TL, respectively. Financing through a local bank can amount to a maximum of 15 million TL.

a. Model an LP by hand.

b. Solve using Excel.

c. What happens to the optimal solution if the bank can only provide 10% less financing?

How much (if any) the collected tax is going to change? Answer this question using a

sensitivity report analysis.

d. The government is planning to increase the tax for a particular home type, which one

would you recommend? How much can the government increase the tax of that type of home without changing the optimal solution? Comment on the effects of such change.

Question 2: TOK is working on a housing project to maximize the collected tax. The project involves two phases: (I) demolishing substandard houses and (2) building the new houses. The following is a summary of the situation. The number of substandard houses that can be demolished is at most 300. Each house occupies a 0.25-acre lot. The cost of demolishing a condemned house is 2000TL Lot sizes for new single-, double-, triple-, and quadruple-family homes (units) are 0.18, 0.28, 0.4, and 0.5 acres, respectively. Streets, open space, and utility casements account for 15% of available acreage. 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%. The tax to be collected per unit for single, double, triple, and quadruple units is 1,000TL, 1.900TL, 2,700TL, and 3,400TL, respectively. The construction cost per unit for single-, double-, triple-, and quadruple- family homes is 50,000TL, 70,000TL, 130,000TL, and 160,000TL, respectively. Financing through a local bank can amount to a maximum of 15 million TL a. Model an LP by hand. b. Solve using Excel. c. What happens to the optimal solution if the bank can only provide 10% less financing? How much (if any) the collected tax is going to change? Answer this question using a sensitivity report analysis. d. The government is planning to increase the tax for a particular home type, which one would you recommend? How much can the government increase the tax of that type of home without changing the optimal solution? Comment on the effects of such change. Question 2: TOK is working on a housing project to maximize the collected tax. The project involves two phases: (I) demolishing substandard houses and (2) building the new houses. The following is a summary of the situation. The number of substandard houses that can be demolished is at most 300. Each house occupies a 0.25-acre lot. The cost of demolishing a condemned house is 2000TL Lot sizes for new single-, double-, triple-, and quadruple-family homes (units) are 0.18, 0.28, 0.4, and 0.5 acres, respectively. Streets, open space, and utility casements account for 15% of available acreage. 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%. The tax to be collected per unit for single, double, triple, and quadruple units is 1,000TL, 1.900TL, 2,700TL, and 3,400TL, respectively. The construction cost per unit for single-, double-, triple-, and quadruple- family homes is 50,000TL, 70,000TL, 130,000TL, and 160,000TL, respectively. Financing through a local bank can amount to a maximum of 15 million TL a. Model an LP by hand. b. Solve using Excel. c. What happens to the optimal solution if the bank can only provide 10% less financing? How much (if any) the collected tax is going to change? Answer this question using a sensitivity report analysis. d. The government is planning to increase the tax for a particular home type, which one would you recommend? How much can the government increase the tax of that type of home without changing the optimal solution? Comment on the effects of such change