The linear program given below seeks to maximize the objective function 2x1+3x2 subject to the following constraints: x1+2x216,x1+x210,3x1+x224,x10, and x20. a) Draw a diagram that displays the area in which the constraints of the linear program are satisfied. Include the coordinates of each vertex where the boundary of the feasible region meets. b) Find the best possible solution for the linear program, and the corresponding value of the objective function. c) Formulate the dual problem for the linear program described above. d) Solve the dual problem to obtain the optimal solution and the optimal value of the objective function. Then, apply the complementary slackness condition to identify a dual variable that is zero in at least one optimal solution