solve completelyie both phase and phase via the simplex met

solve completely(i.e. both phase ? and phase ?)via the simplex method the following problem

all variable in non negative

Solution

if we take subject to equation as matrix:

Find the pivot in the 1st column in the 1st row

Eliminate the 1st column

Find the pivot in the 2nd column in the 2nd row (inversing the sign in the whole row)

Eliminate the 2nd column

Make the pivot in the 3rd column by dividing the 3rd row by 3

Solution set:

x1 = 2 + 17x4 - x5

x2 = - 7x4

x3 = 1 - (11/3)x4 - (1/3)x5

x4, x5 - free

if take x4,x5 is 0,0

then minimize is: x1=2;x2=0,x3=1

         2(2)+3(1)

      =7.