![QUESTION 3: Resource Allocation, Linear Programming (L.P) an d TOC 25 marks] Th e local city council has acquired a block of land for a new social housing development. The councillors have voted unanimously to build a combination of blocks such that the nu houses and apartment sloping nature of the site and infrastructure issues, however, there are limitations on what can be built there. After consulting their engineers and architects, they have decided to limit the number of apartment blocks to 5, and the number of houses to 10. Initial plans have been drawn up for the houses and apartment blocks: each house would accommodate a family of 6, while each apartment block would accommodate 20 people. Each apartment block requires 50 units of labour, 20 units of materials and 2 units of land. Each of the houses would require 10 units of labour, 5 units of materials and 1 unit of land There are 350 units of labour available, 200 units of materials and 15 units of land. Formulate the decision problem as an LP, providing a table format, mathematical formulation, and graph. a (10 marks) Determine the best combination of apartment blocks and houses to meet the requirements detailed above. Show the optimal solution on your graph and briefly explain why this is optimal. How many people can be accommodated in this development?(4 marks) b With brief reasons, how much extra accommodation could be provided if: c The council was able to source another unit of materials from a local supplier? An extra unit of land was made available? i. ii. The building engineer has found a way to reduce the labour required for each apartment block to 40 units of labour? If the architect can design houses to fit 8 rather than 6 people with the same resources, land and labour, then would you build more houses? A portion of the sensitivity report is provided below which can be used if needed. iii. iv. Reduced Objective Allowable Allowable Name Cost Coefficient Increase Decrease Cell CS4 Apprt blocks SD$4 Houses 20 1E+30 (8 marks) d. Finally offer some comments on the merits and drawbacks of using LP for resource allocation decisions on its own, and with complementary frameworks such as Theory of Constraints (TOC). (3 marks)](https://media.cheggcdn.com/media%2F0e4%2F0e49c510-1d12-485f-9afb-2518fcde8466%2Fimage.png)
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QUESTION 3: Resource Allocation, Linear Programming (L.P) an d TOC 25 marks] Th e local city council has acquired a block of land for a new social housing development. The councillors have voted unanimously to build a combination of blocks such that the nu houses and apartment sloping nature of the site and infrastructure issues, however, there are limitations on what can be built there. After consulting their engineers and architects, they have decided to limit the number of apartment blocks to 5, and the number of houses to 10. Initial plans have been drawn up for the houses and apartment blocks: each house would accommodate a family of 6, while each apartment block would accommodate 20 people. Each apartment block requires 50 units of labour, 20 units of materials and 2 units of land. Each of the houses would require 10 units of labour, 5 units of materials and 1 unit of land There are 350 units of labour available, 200 units of materials and 15 units of land. Formulate the decision problem as an LP, providing a table format, mathematical formulation, and graph. a (10 marks) Determine the best combination of apartment blocks and houses to meet the requirements detailed above. Show the optimal solution on your graph and briefly explain why this is optimal. How many people can be accommodated in this development?(4 marks) b With brief reasons, how much extra accommodation could be provided if: c The council was able to source another unit of materials from a local supplier? An extra unit of land was made available? i. ii. The building engineer has found a way to reduce the labour required for each apartment block to 40 units of labour? If the architect can design houses to fit 8 rather than 6 people with the same resources, land and labour, then would you build more houses? A portion of the sensitivity report is provided below which can be used if needed. iii. iv. Reduced Objective Allowable Allowable Name Cost Coefficient Increase Decrease Cell CS4 Apprt blocks SD$4 Houses 20 1E+30 (8 marks) d. Finally offer some comments on the merits and drawbacks of using LP for resource allocation decisions on its own, and with complementary frameworks such as Theory of Constraints (TOC). (3 marks)
