Basis Index Set: Bind \"I\" Bind1 = 1 3 4 Select as the entering variable column

Question

Basis Index Set: Bind "I" Bind1 = 1 3 4 Select as the entering variable column 2 (e.g. x1) Select based on the computation on the first page of these notes the leaving column to be column 2 (e.g. x2) What is the coefficient matrix of the basic variables for the new Bind (call it B) Note these are taken in order from the "current" tableau. B = What is the inverse of this matrix B? inv(B) = What is the new tableau for this BFS solution? This results from inv(B)*T (where T is the current tableau matrix). Find all the basic solutions (BS) to the system of equations check that each one is a solution to the original problem. which BS are also basic feasible solutions (BFS)?

Explanation / Answer

2> the system of linear equation have 3 variables and we have two equations :

the equation are :

3x1 + 6x2 - 4x3 =5 , ---------->(1)

2x1 - x2 + 6x3 = 7 , ----------->(2)

as we have to equation and 3 variables so e'll have infinite many solutions :

the above equations could be riten as :

6x2 - 4x3 =5 -3x1 , ---------->(3)

x2 + 6x3 = 7 -2x1 , ---------->(4)

solving (3) and (4) for x2 and x3 in terms of x1

=> x2 = 29/16 - 13(x1)/16

    x3 = 47/32 - 15(x1)/32

and x1 = x1

for all x1 E R

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