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Questions of the 2019 Higher Education Society Cup National College Student Mathematics Modeling Competition Question E "Small Profits and Rapids" Analysis

Question E "Small profit but quick turnover" analysis

"Small profits but quick turnover" is a strategy to expand sales by reducing the profit per unit of goods to increase sales, thereby allowing merchants to make more profits. For products with elastic demand, when the price of the product drops, if the increase in demand (and thus sales) is greater than the decrease in price, it will lead to an increase in total revenue. In actual business management, the principle of "small profit but quick turnover" is widely used. (/item/small profit but quick turnover)

Attachment 1 and Attachment 2 are the sales records of a shopping mall from November 30, 2016 to January 2, 2019. Attachment 3 is the discount information table, Attachment 4 is the product information table, and Attachment 5 is the data description table. Please build a mathematical model based on this batch of data to solve the following problems:

  1. Calculate the daily turnover and profit margin of the mall from November 30, 2016 to January 2, 2019 (Note: Due to unknown reasons, the cost price of non-discounted goods in the data is missing. Generally, the profit margin of the retailer is between 20% and 40%).
  2. Establish appropriate indicators to measure the daily discounts of the mall and calculate the daily discounts of the mall from November 30, 2016 to January 2, 2019.
  3. Analyze the relationship between discount strength, commodity sales and profit margin.
  4. If we further consider the major categories of goods, what changes will the relationship between discount strength and commodity sales and profit margins?

Attachment 1, Attachment 2: Sales Record

Attachment 3: Discount information form

Attachment 4: Product Information Table

Attachment 5: Data Description Table