4. A batch of goods is divided into many packages of different sizes, with each package, including its packaging, weighing no more than 350 kilograms. The total weight of this batch of goods, including packaging, is 13500 kilograms. Now, a truck with a load capacity of 1500 kilograms is used to transport these goods. If it can always be fully loaded, then it can be transported in 9 trips. However, the goods must be loaded onto the truck in whole packages, so it may not always be fully loaded. Prove that there is a way to transport all the goods in at most 11 trips.
Solution
(提示: First, load the first truck as much as possible, until it reaches 1500 kilograms, but adding one more package would exceed 1500 kilograms, and place this package aside. Then handle the second, third, ... trucks in the same way, until all 8 trucks are loaded. At this point, the total weight of the goods on the 8 trucks and the goods set aside has exceeded . The remaining weight, which is no more than 1500 kilograms, can be loaded onto the 9th truck, and the 8 packages set aside, since , can be loaded onto two trucks.)
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