Work individually. Show all your work. Write legibly. Arrange your responses in the same order as the problems listed below and staple all the pages together. Do not scan and upload your response to Blackboard. Please submit your responses in class. Late assignments will not be graded. 1. Consider the following linear program. Maximize 10x+3y s.t. 2x+y10y2x2x,y0 - Graph the feasible region. Report the optimal solution. - Assume the initial solution as x(0)=(1,6) and x=(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 x(0),x(1), and x 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 x(0),x(1), and x on the graph. - Assume the initial solution as x(0)=(0,2) and the in the next two iterations your solution is x(1)=(0,10), and x(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. Work individually. Show all your work. Write legibly. Arrange your responses in the same order as the problems listed below and staple all the pages together. Do not scan and upload your response to Blackboard. Please submit your responses in class. Late assignments will not be graded. 1. Consider the following linear program. Maximize 10x+3y s.t. 2x+y10y2x2x,y0 - Graph the feasible region. Report the optimal solution. - Assume the initial solution as x(0)=(1,6) and x=(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 x(0),x(1), and x 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 x(0),x(1), and x on the graph. - Assume the initial solution as x(0)=(0,2) and the in the next two iterations your solution is x(1)=(0,10), and x(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