# soln

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```					03Mar2010                Sultan, A., 1.2 Formulation of linear programs, Example 1.1, p 3
Diet         Minimum cost of diet unit (or portion) ?      Solution: Example 2.6, p 29
X * = (1.5, 1), z * = 1.3\$
Content, g (per unit) Protein         Fat     Carbohydr. Cost (\$)
Food A         20          12          30          0.6
Food B         30           6          15          0.4
Minimum requirements          60          24          30                            It's better to "transpose" this problem.

Cost          0.6           0.4
Food A        Food B
Protein       20            30                      60
Fat           12             6                      24
Carbohydrat   30            15                      30                 One more step (without knowing what we're doing)...

Cost            0.6         0.4         1.3     minimize                           Solver model
x1          x2                                                              1.3
Protein         20           30         60                      60                         2
Fat             12            6         24                      24                    TRUE
Carbohydrat     30           15         60                      30                       100
Solution       1.5           1
"transpose" this problem.

ep (without knowing what we're doing)...
03Mar2010                  Sultan, A., 1.2 Formulation of linear programs, Example 1.2, p 5
Cars         Maximum profit ?                              Solution: Example 2.7, p 29
X * = (30, 100), z * = 42000\$
Assembly Finishing        Profit      At least
Model A          4h           6h         400        20 units
Model B          6h           3h         300        30 units
Availability     720 h         480 h

Model A     Model B
Assembly         4           6                       720
Finishing        6           3                       480
Model A          1           0                       20
Model B          0           1                       30

Profit           400          300       42000     maximize                            Solver model
x1           x2                                                           42000
Assembly           4           6          720                    720                          2
Finishing          6           3          480                    480                     TRUE
Model A            1           0          30                     20                      TRUE
Model B            0           1          100                    30                         100
Solution        30          100
03Mar2010                Sultan, A., 1.2 Formulation of linear programs, Example 1.3, p 7
Transportation              Minimum cost ?                 Solution: Example 2.7, p 29
z * = 1930\$
Cost    Distributor 1 Distributor 2 Distributor 3 Distributor 4 Supply
Warehouse 1      22            36            24            23         20
Warehouse 2      31            19            32            26         30
Warehouse 3      25            25            16            22         50
Demand         20            30            30            20
Minimum
Units   Distributor 1 Distributor 2 Distributor 3 Distributor 4                     Supply     Cost Solver model
Warehouse 1      20             0             0        3.553E-15      20      =            20       1930           1930
Warehouse 2       0            30             0             0         30      =            30                        12
Warehouse 3       0        7.105E-15         30            20         50      =            50                   FALSE
20            30            30            20                                                   FALSE
=             =             =             =                                                       100
Demand         20            30            30            20
Solver model

```
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