Quiz_1A_2023FA_Solution

Question 2: Solve the following linear optimization problem using the primal simplex method. Min 2 x 1 − x 2 + x 3 s .t . 3 x 1 + x 2 + 2 x 3 ≤ 60 ; x 1 − x 2 + 2 x 3 ≤ 10 ; x 1 + x 2 − x 3 ≤ 20 ; x 1 , x 2 , x 3 ≥ 0. Note that, you can submit your solution in excel file. However, you need to include the detailed steps in the simplex algorithm for solving the LO problem. The initial tableau for the min LO is: Based on the above tableau, x2 enters the basis and s3 leaves the basis. Perform the pivot, we obtain: The optimal solution is x2=20, Z=-20. Z -2 1 -1 0 0 0 S1 3 1 2 1 0 0 60 S2 1 -1 2 0 1 0 10 S3 1 1 -1 0 0 1 20 Z -3 0 0 0 0 -1 -20 S1 2 0 3 1 0 -1 40 S2 2 0 1 0 1 1 30 X2 1 1 -1 0 0 1 20