The Lewisham City Council is faced with a severe budget shortage due to unexpected social costs from the Covid-19 pandemic. The council is now reconsidering an earlier proposal submitted by a property developer. This proposal seeks to demolish existing council buildings in the Catford area and replace them with modern residential developments that can attract     higher council tax rates. The developer can build one-bedroom, two-bedroom, three-bedroom or four-bedroom houses. The council must, therefore, determine how many existing buildings to demolish and how many units of the new buildings to put up. The following information is available about the project: 

- The Catford area has about 250 units of council buildings that can be demolished. The cost of demolishing a building is budgeted to be £2500. Each building occupies a 0.30-acre lot. 

- The table below shows the construction cost and the budgeted lot size required for each type of new house. It also shows the expected annual council tax that could be generated from each type of property. 

 

- Construction policies require that 10% of the available acreage after demolishing be reserved for streets, utility instalments and other emergency facilities. Additionally, at least 10% of the new units should be four-bedroom houses. At least 5% of the new units should be two-bedroom houses. Finally, at most 45% of the new units should be two- and three-bedroom houses. 

- The council can access a maximum of £12 million financing facility with a High Street bank. 

 

The council will want to determine the maximum annual council tax that could be generated after this project. Answer the following questions: 

a. Formulate a linear programming model to determine the total number of each type of new housing unit to be built and the number of old buildings to be demolished to maximise council tax generated. 

b. Formulate and solve the LP model using Excel solver. How much tax will the current plan generate? 

c. Using the sensitivity report, answer the following questions: [8] i. Why are there no three-bedroom houses to be built in the current plan? Advise the council on two ways to achieve positive units of three-bedroom units in the optimal plan. 

ii. What will be the effect on the optimal solution and tax if the council tax for a four-bedroom unit is set equal to that for a three-bedroom house? 

iii. The council is considering increasing council taxes by 10%. What will be the impact of this policy on the optimal solution and total tax generated? 

d. In the report, describe your findings.

 

Transcribed Image Text:

House Type One-bedroom Two-bedroom 0.30 0.35 Three- Lot size (acre) bedroom 0.15 Four-bedroom 0.40 Unit cost (£) 45,000 65,000 120,000 150,000 Council tax (£) 1,292.63 1,508.87 1,723.51 1,938.95 House Type One-bedroom Two-bedroom 0.30 0.35 Three- Lot size (acre) bedroom 0.15 Four-bedroom 0.40 Unit cost (£) 45,000 65,000 120,000 150,000 Council tax (£) 1,292.63 1,508.87 1,723.51 1,938.95

Answer rating: 100% (QA)

SOLUTION a Linear programming model formulation Let x1 Number of onebedroom houses to be built x2 Number of ... View the full answer