Mira and Marnie recently received a gift from their parents 6000 pounds of chocolate bars and 2000 pounds of candies in total. So, they decided to go into business selling Trick-or-treat packages at Halloween party. They can sell a package with 3 pounds of chocolate bars and 2 pounds of candies for $20. Also, they can purchase a sweet bundle for $30 to replenish inventory. The bundle is comprised of 3 pounds of chocolate bars and 4 pounds of candies.

(a) (8 pts) Develop an LP model to determine how many bundles and packages should Mira & Marnie buy and sell to maximize their profit. (Define the decision variables precisely to receive the full credit.)

(b) (8 pts) Draw a graphical solution and point out the optimal solution. Specify the objective function, feasible region, constraints, and the optimal solution to receive full credits.