solve all parts with detailed solutions showing all steps

In this question, we solve the problem (1) in a different way. (a) Suppose we take x1,x2, and x4 as basic variables, and denote by B the corresponding basis matrix. Change B to the identity matrix I using row operations. That is, change121221132131396totheform100010???001???. (b) Based on (a), find the optimal value for the dual linear program of (1) using the dual simplex method. (c) How do you construct an optimal solution to (1) using the result in (b)? 3x1x23x3+x4x1+2x2x3+x4=32x12x2+3x3+3x4=9x1x2+2x3x4=6xi0,i=1,2,3,4