A council has a brown-field sites designated for social housing. After allowing for roads and parks...

Question

A council has a brown-field sites designated for social housing. After allowing for roads and parks it has an area of XXXXXXXXXXm
2
for social housing. The housing association intends to build a mixture of flats, two-bedroom houses, three-bedroom houses, and shops (which include a living space) on this site.

The housing association wishes to maximise the number of people that can be housed but has 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 be flats;

buildings containing the flats (
i.e
a “block”) must have two storeys and every flat must have 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 are given in the following table.

Housing type

Flat Two-bedroom house Three-bedroom house Shop

Average number of inhabitants

XXXXXXXXXX

Ground floor area (m
2
) 75

60

80 120

Formulate a linear programme to help the council decide on a optimal strategy.

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Baljit · Accepted Answer

Decision variables:-
Let be the number of flats, two-bedroom houses, three-bedroom houses and shops in premise of 150,000 m2 . 
Such that
x1,x2,x3,x4 > 0
Constraints:-
1.  All variables must be positive
x1,x2,x3,x4 > 0
2. Total area of all for social housing must be less than 150,

A council has a brown-field sites designated for social housing. After allowing for roads and parks it has an area of XXXXXXXXXXm 2 for social housing. The housing association intends to build a...

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