Consider the following linear program. Maximize 10x + 3y s.t. 2x + y 10 y - 2x 2 x,y 20 Graph the feasible region. Report the optimal solution. Assume the initial solution as (0) = (1,6) and Ar = (1,0). Is this an improving and a feasible direction? Show all your work. If it is an improving and a feasible direction, then find the next best solution in the improving search. Is the new solution a local optimum, global optimum, or neither? Show (0), 2(), and Az on the graph. What is the gradient? Is the gradient an improving and a feasible direction at (0,2)? If it is an improving and a feasible direction, then find the next best solution in the improving search. Is the new solution a local optimum, global optimum, or neither? Show (0), 2(), and Ar on the graph. Assume the initial solution as (0) = (0, 2) and the in the next two iterations your solution is 2() = (0, 10), and r(2) = (2,6). Find the improving and feasible direction to move from one iteration to another. Classify these solutions as local optimum, global optimum, or neither.