You and your friends are driving to Tijuana for spring break. You discover that you are bringing a lot of gear, luggage, and people and may have to take multiple cars. You have n items you want to bring. Each item weighs between 1 pound and 1000 pounds. Each car can hold at most 1000 pounds. You want to determine how to assign items to cars so that you use the minimum number of cars.1. State the input and output conditions for this problem as precisely as possible.2. If you have n items what is the maximum number of cars you will need? If you haven items what is a lower bound on the minimum number of cars you will need?3. Your friend Alice has a plan to pack the cars. She suggests placing each item in the first car that it will fit in. She calls this the first-fit algorithm. Come up with a counter example to show this algorithm will not produce the least number of cars.4. Your friend Bob has a plan to pack the cars. He suggests placing each item in the car it fits best in. He thinks an item fits best in a car if it leaves the car with the least amount of free space. He calls this the best-fit algorithm. Come up with a counter example to show this algorithm will not produce the least number of cars.