Consider the following LP Max Z 3x1x25x3 st x12x2x32 x1x31

Consider the following LP.

Max Z = 3x1-x2+5x3 st. x1-2x2+x3<=5 , 4x2+x3>=2 , -x1+x3=1 , x1,x2,x3 >=0

A) Find the dual of this LP

B) After adding slack variables s1, subtracting an excess variable e2, adding artificial variables a2 and a3, Row 0 of the LP\'s optimal tableau is found to be z+4x1+3e2+(M-6)a2 + (M+9)a3 =0

Find the optimal solution of the dual of this LP.

Solution

a)

max Z = 5y1 + 2y2 + t3

st.

3y1 - y2 + 5y3 < 1