44 yuan is the flower of 99 yuan.

First of all, let's review the discount strategy adopted by merchants last year. The so-called "XXX as XXX yuan flower", such as 44 as 99 yuan flower, "is to spend 44 yuan to buy a shopping voucher worth 99 yuan, and then spend it in the mall with the shopping voucher. For example, if you buy a pair of shoes with a price tag of 109 1 yuan, you can spend1kloc-0/44 yuan Buy199 yuan Shopping Voucher 1089 yuan, and then pay the remaining 2 yuan in cash. At this time, the actual payment was 486 yuan. As far as the formula is concerned, it is:

For goods with a price tag of P yuan, let P = 99 n+m, where M and N are integers, and consumers need to pay P 1 = 44n+m yuan.

However, if the m of commodity price is close to 99, we can actually save money. For example, you can of course buy a 1 1 shopping voucher in 99 yuan and a1/79 yuan dress in 90 yuan. At this time, you spent 574 yuan. However, if you directly buy the 12 99 yuan shopping voucher, you only need to spend 528 yuan. After buying clothes, 9 yuan will still be left on the shopping voucher (of course, 9 yuan won't give you change). In other words, when m > 44 points, that is, the price is close to an integer multiple of 99, it is more cost-effective to buy one more shopping voucher. At this time, its cost is P2 = 44n+44 yuan.

According to the above analysis, we invite the mathematical software Matlab to draw the change of the equivalent discount rate of this promotion method in the price range of 1 to 2000, as shown in the following figure. In fact, the die-hards have analyzed this discount strategy in detail in the article "No matter how you play, you can't beat the merchants". Interested readers can review it.

99 yuan minus 55 yuan.

After a brief review of the previous promotion methods of merchants, this paper focuses on the analysis of the more popular discount schemes this year. In order to correspond to the above, take "99 MINUS 55" as an example. In fact, the analytical thinking is similar. The price of the same pair of shoes is 109 1 yuan. Because it is * * * "full" of 1 1 99, it is necessary to subtract 1 1 55, which means that the actual payment is 486 yuan. But unfortunately, if M > is met in the case of 44, consumers will have no more cost-effective shopping strategy. When the commodity price is close to the integer multiple of 99, there is no way to "reduce" because the number of times of "full" 99 has not changed. Generally speaking, "over 99 minus 55" is the actual payment P3 = 44n+m. According to this formula, we can also get the change of discount rate in the price range of 1 to 2000, which is equivalent to this promotion method.

The more cunning place for merchants is pricing.

Maybe you already think that "over 99 minus 55" is an upgraded version of "44 when 99 flowers", which looks equally attractive, but the actual discount has shrunk, because you can't adopt a more cost-effective shopping strategy when the price is close to 99 integer times. Draw the changes of discount rate corresponding to the above two different promotion methods together, and we can clearly find this trend. In the area with m < 44, the red line (full 99 minus 55) and the blue line (44 with 99 flowers) overlap, while in other areas, the actual discount rate of 44 with 99 flowers is obviously lower. In addition to the discount rate becoming obviously ineffective, this year's strategy also makes it easier for businesses to achieve smaller profits by controlling prices. When the merchants set prices last year, it was most favorable to meet the following conditions:

The m of a single commodity is close to 44. As can be seen from the first figure, the peaks with higher discount rate all appear at m = 44.

2. The prices of various commodities should not be too close to the integer multiple of 99.

But it is easy to see that these two requirements are contradictory. Assuming that the unit price of goods can guarantee m = 44, the total price of two goods is 88, which is very close to 99. Buying two goods at the same time will make the discount rate lower.

However, if the merchants adopt the strategy of "over 99 minus 55", the pricing will be much more comfortable this year. At this time, as long as the m of the unit price of the commodity is as close as possible to 99. This not only ensures that the discount rate of customers who buy only one commodity is at the peak, but also ensures that the discount rate of customers who buy multiple commodities at the same time will not drop too much. For example, if the M of two commodities is 98 and 97 respectively, then the M of the total price is 96, and the discount rate is still near the peak.