Question

Walnut Orchard has two farms that grow wheat and corn. Because of different soil conditions, there are differences in the yields and costs of growing crops on the two farms. The yields and costs are sown in the table below. Each farm has 100 acres available for cultivation; 11,000 bushels of wheat and 7,000 bushels of corn must be grown. Use LP to determine a planting plan that will minimize the cost of meeting these demands.

	Farm 1	Farm 2
Corn yield / acre (bushels)	500	650
Cost / acre of corn ($)	100	120
Wheat yield / acre (bushels)	400	350
Cost/ acre of wheat ($)	90	80

Show LP simplex and use lindo model software to solve for Total Cost Acres of farm 1 devoted to Corn, Acres of farm 1 devoted to Wheat, Acres of farm 2 devoted to Corn and Acres of farm 2 devoted to Wheat

Answer 1

Decision variables:

C1 = # of acres of Farm 1 planted in corn

W1 = # of acres of Farm 1 planted in wheat

C2 = # of acres of Farm 2 planted in corn

W2 = # of acres of Farm 2 planted in wheat

MIN 100 C1 + 120 C2 + 90 W1 + 80 W2

SUBJECT TO

2) C1 + W1 <= 100

3) C2 + W2 <= 100

4) 500 C1 + 650 C2 >= 7000

5) 400 W1 + 350 W2 >= 11000

END

Tableau #1
c1     c2     w1     w2     s1     s2     s3     s4     -p          
1      0      1      0      1      0      0      0      0      100  
0      1      0      1      0      1      0      0      0      100  
500    650    0      0      0      0      -1     0      0      7000
0      0      400    350    0      0      0      -1     0      11000
100    120    90     80     0      0      0      0      1      0    

Tableau #2
c1          c2          w1          w2          s1          s2          s3          s4          -p                    
1           0           1           0           1           0           0           0           0           100       
-0.769231   0           0           1           0           1           0.00153846 0           0           89.2308   
0.769231    1           0           0           0           0           -0.00153846 0           0           10.7692   
0           0           400         350         0           0           0           -1          0           11000     
7.69231     0           90          80          0           0           0.184615    0           1           -1292.31  

Tableau #3
c1          c2          w1          w2          s1          s2          s3          s4          -p                    
1           0           0           -0.875      1           0           0           0.0025      0           72.5      
-0.769231   0           0           1           0           1           0.00153846 0           0           89.2308   
0.769231    1           0           0           0           0           -0.00153846 0           0           10.7692   
0           0           1           0.875       0           0           0           -0.0025     0           27.5      
7.69231     0           0           1.25        0           0           0.184615    0.225       1           -3767.31  

for better view

Hey , I downloaded LINDO just now and used for the first time .

here are result

Global optimal solution found.
Objective value:                              3767.308
Infeasibilities:                              0.000000
Total solver iterations:                             2
Elapsed runtime seconds:                          3.95

Model Class:                                        LP

Total variables:                      4
Nonlinear variables:                  0
Integer variables:                    0

Total constraints:                    5
Nonlinear constraints:                0

Total nonzeros:                      12
Nonlinear nonzeros:                   0

                                Variable           Value        Reduced Cost
                                      C1        0.000000            7.692308
                                      C2        10.76923            0.000000
                                      W1        27.50000            0.000000
                                      W2        0.000000            1.250000

                                     Row    Slack or Surplus      Dual Price
                                       1        3767.308           -1.000000
                                       2        72.50000            0.000000
                                       3        89.23077            0.000000
                                       4        0.000000          -0.1846154
                                       5        0.000000          -0.2250000