The number of flats in each block, and other relevant information, is as follows — North Penberthy Housing Association planning blocks Five types have been designed containing

North Penberthy Housing Association is planning a number of blocks of flats. Five types of block have been designed, containing flats of four categories (1 - senior citizens, 2 - single person, 3 - small family and 4-large family).

The number of flats in each block, and other relevant information, is as follows:

.:.

The association wants to build a total of 500 flats with at least 40 in category 1 and 125 in each of the other categories. In the past, high-rise flats have proved unpopular and the association wants to limit the number of storeys in the development - with the average number of storeys at most five, and at least half the flats in blocks of three or fewer storeys. An area of 300 units has been set aside for the development and any spare land will be used as a park. Formulate this problem as a linear programme.

SOLUTION:

The decision variables are the number of blocks of each type to build. Let A be the number of blocks of type A built, B the number of blocks of type B and so on.

The objective is to minimise the total cost of the development.

Minimise: 2.08A + 3.2B + 3.0C + 4.8D + 4.8E

There must be a total of 500 flats, so, adding the number of flats in each block gives:

7A + 9B + 10C + 14D + 15E = 500

The minimum numbers of flats in each category is specified, so adding the number of flats of category 1 gives: