3. Shipping Efficiently: A trucking company is responsible for shipping a large number of boxes that require many trips from New York to Boston each day. Each truck has a limit of W on the maximum amount or weight it is allowed to carry. Boxes arrive at the New York depot one at a time and each package has a weight of wi. The depot is small and only one truck can be loaded at a time. Company policy is that boxes must be shipped in the order they arrive, since customers might get upset if they saw a box that arrived later get to Boston earlier than one they sent earlier. Thus, the company uses a simple greedy algorithm for packing the boxes onto a truck. Pack the boxes in the order in which they arrive and once a box does not fit then send the truck on its way. The company asks you to determine if they can do better. E.g., perhaps they could reduce the number of trucks needed by sometimes sending off a truck that is less full but could allow later trucks to be better packed. A. Prove company's algorithm always ships the packages in the fewest trucks. B. Analyze the algorithm's complexity. 3. Shipping Efficiently: A trucking company is responsible for shipping a large number of boxes that require many trips from New York to Boston each day. Each truck has a limit of W on the maximum amount or weight it is allowed to carry. Boxes arrive at the New York depot one at a time and each package has a weight of wi. The depot is small and only one truck can be loaded at a time. Company policy is that boxes must be shipped in the order they arrive, since customers might get upset if they saw a box that arrived later get to Boston earlier than one they sent earlier. Thus, the company uses a simple greedy algorithm for packing the boxes onto a truck. Pack the boxes in the order in which they arrive and once a box does not fit then send the truck on its way. The company asks you to determine if they can do better. E.g., perhaps they could reduce the number of trucks needed by sometimes sending off a truck that is less full but could allow later trucks to be better packed. A. Prove company's algorithm always ships the packages in the fewest trucks. B. Analyze the algorithm's complexity