The Waltham Forest 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 5 in the Waltham Forest 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 Waltham Forest 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. - Table 3 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. Table 3: Cost & lot size requirement

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

- 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. [7] b. Formulate and solve the LP model using Excel solver. How much tax will the current plan generate? [8] c. Using the sensitivity report, answer the following questions: [8] 6 i. In your optimal solution, are any types of housing units not being built? Recommend two strategies to the council for increasing the numbers of this type of unit. 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, summarise answers to the above questions and discuss any additional insights that would support decision making [7]