Project #68475 - homework questions stat 315, 4 questions

 

1.      Answer the following questions using the following problem and its managerial summary solution.

MAX               8X1 + 9X2 + 10X3,

S.T.,     3X1+2X2+2X3 < 2250, 4X1+ 4X2+ 6X3 < 3600, X1+ X2+2X3 < 950, X1+X2 < 800,

all variables are non-negative, and the following managerial information are given:             (40%)

                        Solution           Total                Allowable        Allowable

Variable                       Profit   Profit               Min c(j)           Max c(j)

X1                   0          8.0            0                 -M                   9.0

X2                   800.     9.0       7200.0             8.00                 M

X3                   66.67   10.0     666.67             0                      13.5

 

            Objective         Function          (Max.) =          7866.67                                              

               Left Hand                                       Shadow                       Allowable   

Constraint                   Slack/Surplus              Price                Min. RHS    Max. RHS

C1       1733.33          516.67                         0                      1733.33           M

C2       3600               0                                  1.67                 3200                3650

C3          933.33          16.67                           0                      933.33             M

 

C4          800               0                                  2.33                 750                  900

 

1.1  Construct the dual problem

1.2  What is the solution and optimal value of the dual problem? Why?

 

2. Solve the following LP problem:

 

 Maximize 3X1 + 2X2 + 3X3

 

     Subject to: 4X1 + 3X2 + X3 £12,    

all variables Xi's  ³ 0   

 

3.  Explain in words, how do you use your LINDO package to solve the following system of equations:

 

            2X1 + 3X2 + X3 = 4

            X1 + X2 - X3 = 3

            2X1 - 2X2 - X3 =1

Subject Mathematics
Due By (Pacific Time) 04/26/2015 11:59 pm
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