3.31 by changcheng2

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									                              Atlantic Standard Homes
                                       Problem 3-31
Original Model:




        X1 = the number of Tropic homes built
        X2 = the number of Sea Breeze homes built
        X3 = the number of Orleans homes built
        X4 = the number of Grand Key homes built

        MAX 40,000X1 + 50,000X2 + 60,000X3 + 80,000X4
        S.T.   .20X1 +    .27X2 +      .22X3 +     .35X4    20   (Acres)
                  X1 +       X2                             40   (One story)
                            X2 +         X3 +        X4     50   (3+ BR)
                  X1                                        10   (Min Trop.)
                             X2                             10   (Min Sea Br.)
                                          X3                10   (Min Orleans)
                                                      X4    10   (Min Gr. Key)
                           All X's  0 and integer
                            Atlantic Standard Homes
                                     Problem 3-31
                           Tropic Sea Breeze   Orleans Grand Key
                              29         11        35        10
                                                                        Total
Profit                    40,000     50,000     60,000    80,000    4,610,000 Max
Lot Size                     0.20       0.27       0.22      0.35          20 <=
One Story                       1          1                               40 >=
3+ Bedrooms                                1         1         1           56 >=
Minimum - Tropic                1                                          29 >=
Minimum - Sea Breeze                       1                               11 >=
Minimum - Orleans                                    1                     35 >=
Minimum - Grand Key                                            1           10 >=


                       Stories and Bedrooms
                            Tropic Sea Breeze   Orleans Grand Key
Story                            1          1         2         2
Bedrooms                         2          3         3         4




               Change tolerance to 0.5%
    Answer
a   Profit               Tropic Sea Breeze   Orleans Grand Key
             4,610,000      29          11        35        10
20
40
50
10
10
10
10
                                            Atlantic Standard Homes

                                         Tropic Sea Breeze     Orleans Grand Key
                                         30.00      10.00       35.00      10.00
                                                                                       Total
    Profit                              40,000     50,000      60,000    80,000    4,600,000 Max
    Lot Size                               0.20       0.27        0.22      0.35          20 <=
    One Story                                 1          1                                40 >=
    3+ Bedrooms                                          1          1         1           55 >=
    Minimum - Tropic                          1                                           30 >=
    Minimum - Sea Breeze                                 1                                10 >=
    Minimum - Orleans                                               1                     35 >=
    Minimum - Grand Key                                                       1           10 >=

                                    Stories and Bedrooms
                                          Tropic Sea Breeze    Orleans Grand Key
    Story                                      1          1          2         2
    Bedrooms                                   2          3          3         4




    Answer
b              Profit                  Tropic Sea Breeze      Orleans Grand Key
                        4,627,273        30.00    10.00          35.45    10.00

    Round Orleans model                                           35
    Replace with rounded Orleans
             Profit             Tropic Sea Breeze             Orleans Grand Key
                    4,600,000     30.00    10.00                 35.00    10.00
Solution is feasible, but total profit is decreased by   10,000
20
40
50
10
10
10
10
                                            Atlantic Standard Homes

         Add the following constraints:
         X1 - 12Y1  0
         X2 - 12Y2  0
         X3 - 12Y3  0
         X4 - 12Y4  0
         Y1 + Y2 + Y3 + Y4  3



Opt                             Tropic Sea Breeze   OrleansGrand Key Y1       Y2 Y3 Y4
                                   30         12        33       10 1          1 1 -

      Profit                    40,000    50,000    60,000    80,000
      Lot Size                     0.20      0.27      0.22      0.35
      One Story                       1         1
      3+ Bedrooms                               1        1         1
      Minimum - Tropic               1
      Minimum - SB                             1
      Minimum - Orleans                                  1
      Minimum - GK                                                 1
Y     12 for Tropic                  1                                  -12
Y     13 for SB                                1                              -12
Y     14 for Orleans                                     1                          -12
N     15 for GK                                                    1                      -12
      At least 3 has 12 units                                            1     1     1      1


      Stories and Bedrooms
                                Tropic Sea Breeze   OrleansGrand Key
      Story                          1          1         2        2
      Bedrooms                       2          3         3        4
  Answer
c Profit                     Tropic Sea Breeze   OrleansGrand Key
            4,580,000            30         12        33       10
  There are alternative solution???????
    Total
4,580,000   max limit
       20   <= 20
       42   >= 40
       55   >= 50
       30   >= 10
       12   >= 10
       33   >= 10
       10   >= 10
       18   >=    0
        0   >=    0
       21   >=    0
       10   >=    0
        3   >=    3
Microsoft Excel 10.0 Answer Report
Worksheet: [LPA - Problem 31.xls]Input - c
Report Created: 11/1/2004 11:34:11 AM


Target Cell (Max)
    Cell          Name              Original Value    Final Value
  $K$6 Profit Total                     4,580,000        4,580,000


Adjustable Cells
   Cell          Name               Original Value    Final Value
  $C$4 Tropic                                  30               30
  $D$4 Sea Breeze                              10               12
  $E$4 Orleans                                 32               33
  $F$4 Grand Key                               12               10 alternative solution - see worksheet Questio
  $G$4 Y1                                       1                 1
  $H$4 Y2                                     -                   1
  $I$4 Y3                                       1                 1
  $J$4 Y4                                       1              -


Constraints
   Cell            Name               Cell Value        Formula        Status Slack
  $K$7 Lot Size Total                          20    $K$7<=$M$7      Binding        0
  $K$8 One Story Total                         42    $K$8>=$M$8      Not Binding   2
  $K$9 3+ Bedrooms Total                       55    $K$9>=$M$9      Not Binding   5
  $K$10 Minimum - Tropic Total                 30    $K$10>=$M$10    Not Binding 20
  $K$11 Minimum - SB Total                     12    $K$11>=$M$11    Not Binding   2
  $K$12 Minimum - Orleans Total                33    $K$12>=$M$12    Not Binding 23
  $K$13 Minimum - GK Total                     10    $K$13>=$M$13    Binding     -
  $K$14 12 for Tropic Total                    18    $K$14>=$M$14    Not Binding 18
  $K$15 13 for SB Total                          0   $K$15>=$M$15    Binding     -
  $K$16 14 for Orleans Total                   21    $K$16>=$M$16    Not Binding 21
  $K$17 15 for GK Total                        10    $K$17>=$M$17    Not Binding 10
  $K$18 At least 3 has 12 units Total            3   $K$18>=$M$18    Binding     -
  $K$10 Minimum - Tropic Total                 30    $K$10>=$M$10    Not Binding 20
  $K$11 Minimum - SB Total                     12    $K$11>=$M$11    Not Binding   2
  $K$12 Minimum - Orleans Total                33    $K$12>=$M$12    Not Binding 23
  $K$13 Minimum - GK Total                     10    $K$13>=$M$13    Binding     -
  $C$4 Tropic                                  30    $C$4=integer    Binding     -
  $D$4 Sea Breeze                              12    $D$4=integer    Binding     -
$E$4   Orleans      33   $E$4=integer   Binding   -
$F$4   Grand Key    10   $F$4=integer   Binding   -
$G$4   Y1            1   $G$4=binary    Binding   -
$H$4   Y2            1   $H$4=binary    Binding   -
$I$4   Y3            1   $I$4=binary    Binding   -
$J$4   Y4          -     $J$4=binary    Binding   -
n - see worksheet Question c - alternate
                                               Atlantic Standard Homes

Opt                             Tropic Sea Breeze     OrleansGrand Key Y1 Y2 Y3             Y4
                                   30         10          32       12 1 -     1              1

      Profit                    40,000      50,000    60,000    80,000
      Lot Size                     0.20        0.27      0.22      0.35
      One Story                       1           1
      3+ Bedrooms                                 1        1         1
      Minimum - Tropic                  1
      Minimum - SB                               1
      Minimum - Orleans                                    1
      Minimum - GK                                                   1
Y     12 for Tropic                     1                                 -12
N     13 for SB                                  1                              -12
Y     14 for Orleans                                       1                          -12
Y     15 for GK                                                      1                      -12
      At least 3 has 12 units                                              1     1     1      1


      Stories and Bedrooms
                                Tropic Sea Breeze     OrleansGrand Key
      Story                          1          1           2        2
      Bedrooms                       2          3           3        4


               Change to Max. X4




                  Add this constraint
  Answer
c Profit                     Tropic Sea Breeze   OrleansGrand Key
            4,580,000            30         10        32       12
  There are alternative solution???????
    Total
4,580,000   max limit
       20   <= 20
       40   >= 40
       54   >= 50
       30   >= 10
       10   >= 10
       32   >= 10
       12   >= 10
       18   >=    0
       10   >=    0
       20   >=    0
        0   >=    0
        3   >=    3

								
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