Q1. Find the optimal solution of the following linear programing (LP) problem without using the Simplex Algorithm (Hint: Construct the dual model, find its optimal solution without using theSimplex Algorithm and utilize the Complementary Slackness Theorem). (LP):maxz=41+32+63Subjectto41+x2+333021+22+3340x1,x2,x30 Q2. The following LP problem and its optimal final tableau are given as follows. If S1, S2 and S3 are slack variables for constraint 1,2 and 3 respectively, answer the questions below: independently: (LP):maxz=5x1+x2+23st.x1+x2+x366x1+x38x2+x32x1,x2,x30 a) Determine the basic variables from the optimal tableau given above. b) Do the Reduced Cost Analysis for the unprofitable activity (That means how we can make that activity just profitable)