Math Problem Statement

根据某文具商店从批发市场进货A、B两种文具,批发价A种文具12元/件,批发价B种文具8元/件。若该商店售货A、B两种文具的日销售量y(件)与零售价x(元/件)均呈一-次函数关系。(1) 求y与x的函数关系式。(2) 若A种文具的零售价比B种文具的零售价高4元/件,求两种文具每日的销售利润(元)。(3) 若按A种文具的日销售量6件和B种文具每件可获利1元计算,商店计划售销A、B两种文具的数量共120件,所有花费金不超过1200元,并希望全部销售完并获得不低于178元利润。该方案的利润最大?

Solution

It looks like you've uploaded an image with a math problem in it. Let me take a moment to analyze the content and provide a solution.The problem in the image appears to involve a scenario where a store is selling two types of tools, A and B. The cost and sales quantities of these tools are related to a variable, and the task requires solving multiple aspects related to maximizing profits based on given constraints.

Here’s the breakdown of the problem:

  1. Part (1) asks to find the relationship between the quantity of items sold and the price for two types of tools (A and B), given their cost and the quantity sold (represented as yy and xx respectively).
  2. Part (2) requests to determine how the daily profit for two types of tools will change as the price for A increases by 4 yuan compared to B, and the relationship between the quantities sold needs to be modeled.
  3. Part (3) involves maximizing the total profit given the constraints of daily sales for A and B, such as the total number of items sold and the total revenue.

There is also a graph provided that seems to show the relationship between the quantities of items sold.

To assist you in solving these problems, I can guide you step-by-step through each calculation.

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Profit Maximization
Algebra
System of Equations

Formulas

y = mx + b
Profit = Revenue - Costs

Theorems

Linear relationship between variables
Profit maximization under constraints

Suitable Grade Level

Grades 10-12