Please answer all parts with work shown to better help me understand. Thank you!

2. Consider the following problem: Max=2x1x2+3x3; Subject to: x1+x2+x3=3x122+x3>=12x2+x3=0,x2>=0,x3>=0. (i) Develop the dual model and indicate the nature of the dual variables. (ii) Use x1=1.0,x2=0 and x3=2.0 as the primal optimal solution and use the Complimentary Slackness theorem to find the optimal dual solution. Show that the optimal objective function values are equal. (iii) Identify a feasible solution for the primal as well as for the dual problem and validate the weak duality theorem. (iv) Reformulate and show the dual model after you make it ready to be solved using the Lingo software. The dual model developed in part (i) is not in the standard form. (v) Solve it using Lingo and report the solution and validate the optimal dual solution found in part (ii)