Maximize 10zg + 12zp st: TR+ 2z 2 zrp 20, zp2>0 (a) (5 points) Construct the dual problem of the associated LP model (use the LP formulation given before): (b) (3 points) Formulate the dual problem corresponding to the primal problem. However, to plot and solve graphically, focus only on the first two dual variables, which correspond to the first two primal constraints (representing the maximum resource availability). Plot the gradient and the feasible region for this restricted dual problem, clearly indicating all relevant constraints and shading the feasible region. Solve this dual problem graphically, and indicate the values of the variables and the objective function associated with the optimal solution. () (4 points) Solve the dual problem using Gurobi/Python. Include a snapshot of your Gurobi/Python code and obtained results, and discuss the results (both of the dual variables and the dual objective function) and their meaning. How are the dual variables and the dual objective function connected to the primal problem? (d) (5 points) Construct the dual problem of the standard form of the LP model Formulation Decision Variables