Please draw a graph and optimal solution.

5. Consider the linear optimization model Minimize 2x + 4y Subject to 4x + 2y 2 8 3x + 4y 2 12 2x + 33/ S 12 x, y 2 0 (a) Graph the constraints and identify the feasible region. (b) Choose a value and draw a 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, nd the intersection point by solving the corresponding system of two equations. ((1) Label the optimal solution(s) on your graph. (e) Calculate the optimal value of the objective function