Linear Programming The following optimal Simplex table is given for a linear pro

Question

Linear Programming The following optimal Simplex table is given for a linear programming problem where the decision variables are x1 , x2 , x3 and the slack variables are denoted by x4 ,…: max x =7 - 66 x1 -48 x3 -7 x5

subject to x4 =3+2 x1 +3 x3 +1 x5

x2 =1-10 x1 -8 x3 -1 x5

and x1 , x2 , x3 0.

Now let us assume we need to add the following constraint to the problem: 8 x1 +7 x2 +8 x3 6

Now answer the following:

(a) Add this new constraint to the current Simplex table, is this table optimal? (answer: 0 for no, 1 for yes)

(b) What is the optimal solution for this modified problem =

(c) If the table is non-optimal, which variable should leave the basis? (answer: 0 for none, else the index of the variable)

(d) Assume we decide to add a very large number of constraints to the problem should we solve the dual problem (answer: 0) or the primal problem (answer: 1) ?

Explanation / Answer

http://web.mit.edu/15.053/www/AMP-Chapter-03.pdf

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