9. (14 points total) Consider the following linear program: Maximize 2x1+3x2 subject to x1+2x216,x1+x210,3x1+x224,x10, and x20 (a) (5 points) Sketch a plot of the feasible region of the linear program. Your sketch should show the exact coordinates of each vertex (i.e., "corner") on the boundary of the feasible region. (b) (3 points) Determine an optimal solution for the linear program, and the optimal objective function value. (c) (3 points) Write the dual of the above linear program. (d) (3 points) Determine an optimal solution for the dual, and the optimal objective function value. Hint: You may find it helpful to use complementary slackness to identify a dual variable that is equal to zero in some optimal solution