1) (5pts) Given the following Simplex Tableau 3 2 -8 1 1 0 0 0 X3...

reci x x xz si sa sa 52 3 0 0 0 4 5 -5 1 0 0 2 3 0 1 0 loooo 0 0 10+> 1 50 The basic variables have the basic values like, [" o o], [o 1o7 & Tool'. Here in this tableau, x2 has [ool, Sa has [o io] and, Sy has [o o s] so x2, S₃ & S₃ are basic variables in this simple tableau And, all the other variables are non-basic, ie, x x z, S &P are non- basic variables. (6) Minimum most value of the set (-8,0,-5,3,0,0) will be the entering be checked to determine the entering rector. Here, -8 is the most minimum. So, entering vector is xa. Now, as (2,3, 2) all are positive, we have to compute 20 30 10 and the = 10, 10, 5. So minimum is 10 The corresponding row indicates that s will be the departing vector. Now, the intersection of the key row (row of

departing vector) and the key columm (colurm of the entering vector), is the pivot element. Here, 12 is the pirot element To perform one pivot operation, we will divide the key row elements of the given tableau by 2 and this will be the new row of new tableau. The other rows of the new tableau are then computed as follows: Subtract 2 times the key row of the new tableau from the est row elements of the old tableau. And, subtract 3-The times the key row elements of new tableau from the and row of old tableau. New Tableau Basic vara 1. x. To salo A. 0 * x, s, 1 -2 -3 o -7/2 - 2 s, 0 s, P -1 0 1 10 1 -3/2015 0