Consider the following linear programming problem: Max Z = X1 + 5X2 Subject to (1) X1 + X2 = 0 (a) Graph the constraint lines

Consider the following linear programming problem: Max Z = X1 + 5X2 Subject to (1) X1 + X2 <= 5 (2) X1 + 3X2 <= 3 (3) 2X1 X2 >= 0 X1, X2 >= 0 (a) Graph the constraint lines and mark them clearly with the numbers (1), (2) and (3) to indicate which line corresponds to which constraint. Darken the feasible region. Use either the corner points method or the objective function line method to determine the optimal solution(s) and the maximum value of the objective function. Provide all necessary details to justify your answers. (b) There is a single optimal solution to this problem. However, if the objective function had been parallel to one of the constraints, there would have been two alternate/equally optimal solutions (i.e. multiple optimal solutions). If the objective function coefficient of x1 remains at 1, what objective function coefficient of x2 would cause the objective function to be parallel to constraint (2) (i.e. X1 + 3X2 <= 3)? Show your calculations