6. Consider the linear optimization model Maximize 2x + y Subject to x + 2y 8 x - y 5 x,y 20 (a) Graph the constraints and identify the feasible region. (b) Choose a value and draw a dotted line representing all combinations of x and y that make the objective function equal to that value. (c) Determine the optimal solution, (x, y). If the optimal solution is at the intersection point of two constraints, find the intersection point by solving the corresponding system of two equations. (d) Label the optimal solution on your graph. (e) Calculate the optimal value of the objective function.