A ship is to be loaded with containers, and every container is the same size but may have a different weight from other containers. There are n containers and we write wi for the weight of the ith container. The capacity, or maximum weight, that the ship can safely bear is c. Initially, we wish to load the ship with the maximum number of containers.

a) Formulate the problem as an optimization problem with a constraint and an optimization function.

b) A ship with the capacity of 120 tons is to be loaded with containers weighing 80, 35, 20, 30, 45, 60 and 25 tons. Give both the optimal solution and a feasible but non-optimal solution.

C) Formulate a good greedy algorithm to solve this problem.