Take the first month as an example, the current inventory is 0. If the ordering cost is certain, then if the ordering cost is at least 0, the inventory at the end of the month must be 0. To sum up, all the parts ordered in that month were used up in that month. As you can imagine, the effect of inventory on time (days) is zigzag, that is, first order, then gradually consume to zero, then order, and then gradually consume to zero. . . It can be seen that the area surrounded by the intersection of sawtooth wave and X axis is its average inventory, which is proportional to the inventory cost. Order points are also easy to see, and the number of order points is directly proportional to the order cost. It can be seen that the more ordering points, the less inventory cost and the more ordering cost, so there is a compromise. Finally, imagine the sawtooth wave translation, we can see that the inventory at the beginning and end of the month is n(n is less than each order quantity), and the inventory at the beginning and end of the month is 0.

For this problem, if the order number is n, then the order cost is 100n.

The quantity of each order is 2400 pieces /n, the daily inventory cost of each piece is150 * 6/(100 *12 * 30), and the service days of each order are 30 pieces/n.

The average inventory cost per time is the multiplication of the above three items and then divided by 2. Consider the zigzag shape here, and the area of each triangle is equal to half the area of the corresponding rectangle.

Finally, multiplied by the number of orders n, the total inventory cost is 900/n.

So the sum of costs = 100n+900/n, when the two terms are equal, the sum is minimum, and the solution is n=3, that is, the order quantity is 800 and the sum of costs is 600.