4)(15$4)(15$ points)$)$ Consider the following maximization problem:

((,))=[((4))()4))]$((,))=[((4))()4))]$subjectto(+)<=4$(+)<=4$and(+3)<=9.$(+3)<=9.$

a)(5$)(5$ points)$)$ Illustrate the constrained optimization problem using a graph ($($Draw indifference

curves and the constraint set)$)$

b)(5$)(5$ points)$)$ Form the Lagrangian function and state the Kuhn−$-$Tucker conditions.

c)(5$)(5$ points)$)$ Find the solution to the optimization problem.