Meadows Or Malls - Anwering the Unit Problem.

6 variables 12 constraints

a)1.Gr+Gd=300
b)2.Ar+Ad=100
c)3.Mr+Md=150
d)4.Gd+Ad+Md=300
e)5.Ar+Mr=200
f)6.Ar+Gd=100
g)7.Gr=0
h)8.Ar=0
i)9.Mr=0
j)10Gd=0
k)11.Ad=0
l)12.Md=0

ABCFDE    ABCFDG    ABCFDH    ABCFDI    ABCFDJ    ABCFDK    ABCFDL    ABCFEG    ABCFEH    ABCFEI     ABCFEJ      ABCFEK    ABCFEL    ABCFGH    ABCFEI     ABCFEJ     ABCFEK    ABCFEL     ABCFGH    ABCFGJ    ABCFGK    ABCFGL    ABCFHI     ABCFHL    ABCFIJ      ABCFIK     ABCFJK   ABCFJL     ABCFKL   

There are 24 different equations that will be used in solving the problem thus creating 24 matrices, 24 coeffiecient matrices, 24 inverse matrices and 24 constant matrices.

ABCFDE  ( To make  a coefficient list Gr  Gd  Ar  Ad  Mr  Md  at the top, mark 1 in every row for every                    variable you have in each equation)
                Gr  Gd  Ar  Ad  Mr  Md
[300]        [1      1    0    0    0     0]
[100]        [0      0    1    1    0     0]
[150]        [0      0    0    0    1     1]
[100]        [0      1    1    0    0     0]
[300]        [0      1    0    1    0     1]
[200]        [0      0    1    0    1     0]
              (  Coefficient matrix of ABCFDE)

Then multiply both matrices and get an answer matrix.

[400]
[250]
[500]
[250]
[400]
[450]

I continued this process for each matrix multiplying it by a coeffiecient matrix and got all the answer matrixes which are:

ABCF
DE    ABCFDG   ABCFDH   ABCFDI    ABCFDJ    ABCFDK    ABCFDL    ABCFEG    ABCFEH   [400]           [400]          [400]         [400]         [400]         [400]         [400]         [400]         [400]
[250]           [250]          [250]         [250]         [250]         [250]         [250]         [250]         [250]
[500]           [300]          [300]         [300]         [300]         [300]         [300]         [200]         [200]
[250]           [250]          [250]         [250]         [250]         [250]         [250]         [250]         [250]
[400]           [200]          [200]         [200]         [200]         [200]         [200]         [350]         [350]
[450]           [300]          [150]         [300]         [100]         [150]         [    0]         [300]         [100]

ABCF
EI    ABCFEJ      ABCFEK    ABCFEL    ABCFGH    ABCFEI    ABCFEJ     ABCFEK    ABCFEL    [400]         [400]           [400]           [400]         [400]         [400]         [400]         [400]         [400]
[250]         [250]           [250]           [250]         [250]         [250]         [250]         [250]         [250]
[200]         [200]           [200]           [200]         [   0]          [200]         [200]         [200]         [200]
[250]         [250]           [250]           [250]         [250]         [250]         [250]         [250]         [250]
[350]         [350]           [350]           [350]         [300]         [350]         [350]         [350]         [350]
[200]         [100]           [100]           [   0]          [150]         [200]         [100]         [100]         [   0]

ABCF
GH   ABCFGJ   ABCFGK    ABCFGL    ABCFHI    ABCFHL    ABCFIJ      ABCFIK   ABCFJK   [400]         [400]           [400]           [400]         [400]         [400]         [400]         [400]         [400]
[250]         [250]           [250]           [250]         [250]         [250]         [250]         [250]         [250]
[   0]          [   0]           [   0]            [   0]         [   0]          [   0]         [   0]          [   0]         [   0]
[250]         [250]           [250]           [250]         [250]         [250]         [250]         [250]         [250]
[300]         [300]           [300]           [300]         [150]         [150]         [   0]         [    0]         [100]
[100]         [   0]           [100]            [   0]         [   0]          [   0]         [100]         [100]         [100]

ABCF
JL    ABCFKL
[400]         [400]
[250]         [250]
[   0]          [   0]
[250]         [250]
[100]         [100]
[   0]          [   0]


After multiplying the 1st matrix with the coeffiecient matrix I found  the inverse of the coeffiecient matrix and multiplied the inverse by the answer I got when I multiplied the 1st matrix with the coefficient matrix.
There are the final answers in matrix form - Some of the equations didnt have inverses so they could not be finished

ABCFDE    ABCFDG    ABCFDH    ABCFDI    ABCFDJ    ABCFDK    ABCFDL    ABCFEG    ABCFEH      []           []          []         []         []         []         []         []         []
[]           []          []         []         []         []         []         []         []
[]           []          []         []         []         []         []         []         []
[]           []          []         []         []         []         []         []         []
[]           []          []         []         []         []         []         []         []
[]           []          []         []         []         []         []         []         []

ABCFEI     ABCFEJ      ABCFEK    ABCFEL    ABCFGH    ABCFEI     ABCFEJ     ABCFEK    ABCFEL      []         []           []           []         []         [400]         [400]         [400]         [400]
[]         []           []           []         []         [250]         [250]         [250]         [250]
[]         []           []           []         []          [200]         [200]         [200]         [200]
[]         []           []           []         []         [250]         [250]         [250]         [250]
[]         []           []           []         []         [350]         [350]         [350]         [350]
[]         []           []           []         []         [200]         [100]         [100]         [   0]

ABCFGH    ABCFGJ    ABCFGK    ABCFGL    ABCFHI     ABCFHL    ABCFIJ      ABCFIK     ABCFJK   [400]         [400]           [400]           [400]         [400]         [400]         [400]         [400]         [400]
[250]         [250]           [250]           [250]         [250]         [250]         [250]         [250]         [250]
[   0]          [   0]           [   0]            [   0]         [   0]          [   0]         [   0]          [   0]         [   0]
[250]         [250]           [250]           [250]         [250]         [250]         [250]         [250]         [250]
[300]         [300]           [300]           [300]         [150]         [150]         [   0]         [    0]         [100]
[100]         [   0]           [100]            [   0]         [   0]          [   0]         [100]         [100]         [100]

ABCFJL     ABCFKL
[400]         [400]
[250]         [250]
[   0]          [   0]
[250]         [250]
[100]         [100]
[   0]          [   0]

Hosted by www.Geocities.ws

1