A council has a brown-field sites designated for social housing. After allowing for roadsand parks it has an area of 150000 m² for social housing. The housing association intendsto build a mixture of flats, two-bedroom houses, three-bedroom houses, and shops (whichinclude a living space) on this site.The housing association wishes to maximise the number of people that can be housed buthas strict housing requirements:• there must be at least twice as many two-bedroom houses as three-bedroom houses;• at least 10% of the total housing units excluding shops (i.e. flats and houses) must beflats;• buildings containing the flats (i.e a "block") must have two storeys and every flat musthave the same floor space;• shops must be provided at a rate of at least one per 1500 inhabitants.The average number of inhabitants per housing unit and the ground floor area of each aregiven in the following table.Housing typeFlatTwo-bedroom houseThree-bedroom houseShopAverage number of inhabitants Ground floor area (m²)7560801201.53.554Formulate a linear programme to help the council decide on a optimal strategy.

Defining variables : Let a number of flats, two-bedroom houses, three-bedroom houses and shops in…

Answered: Housing type Flat Two-bedroom house…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter5: Network Models

Section5.3: Assignment Models

Problem 12P

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Housing type Flat Two-bedroom house Three-bedroom house Shop Average number of inhabitants Ground floor area (m²) 75 60 80 120 1.5 3.5 5 4 Formulate a linear programme to help the council decide on a optimal strategy.