1 [Total 50 pts] Consider the linear program named (P) below. maxs.t.30x1+12x210x1+6x24x1+8x2xj5x1+4x26030240,j 1.a [20 pts] For B=[A1,A3,A4], where A3 and A4 correspond to the columns of s1 (the slack variable for the first constraint) and s2 (the slack variable for the second constraint), respectively, find the corresponding basic feasible solution and show that the solution is optimal but infeasible for (P). 1.b [15 pts] Apply the dual simplex method to the solution in Part 1.a to find an optimal (fensible) solution for (P) (That is, do NOT solve (P) by the simplex method.) 1.c [15 pts] Construct the dual of (P) and find its optimal solution from the solution in Part 1.b by means of the complementary slackness conditions (That is, do NOT apply the simplex method to solve the dual LP.) 1 [Total 50 pts] Consider the linear program named (P) below. maxs.t.30x1+12x210x1+6x24x1+8x2xj5x1+4x26030240,j 1.a [20 pts] For B=[A1,A3,A4], where A3 and A4 correspond to the columns of s1 (the slack variable for the first constraint) and s2 (the slack variable for the second constraint), respectively, find the corresponding basic feasible solution and show that the solution is optimal but infeasible for (P). 1.b [15 pts] Apply the dual simplex method to the solution in Part 1.a to find an optimal (fensible) solution for (P) (That is, do NOT solve (P) by the simplex method.) 1.c [15 pts] Construct the dual of (P) and find its optimal solution from the solution in Part 1.b by means of the complementary slackness conditions (That is, do NOT apply the simplex method to solve the dual LP.)