Problem 2 (10 pts) You have n items with sizes a1,,an to be packed into some bins. Each bin has capacity V. (a). Formulate an integer program to find the packing method that uses the least number of bins. (Hint: Use Ij to denote whether bin j is used; use xij to denote whether item i should be placed in bin j. This is called bin packing problem.) (b). Now consider a real case where you have items with size 3,4,5,7 and the capacity of each bin is 9 . Formulate the IP in that case. What are the optimal solutions to the IP and its LP relaxation? Is there an integrality gap in this case