"When to Get the Maximum Profit" Quadratic Function PPT Courseware 3

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"When to Get the Maximum Profit" Quadratic Function PPT Courseware 3

Yiyiyi: How to find the optimal value of a quadratic function

Quadratic function y=a(x-h)²+k (a≠0)

Vertex coordinates (h,k)

①When a>0, when x=h, y has a minimum value=k

②When a<0, when x=h, y has the maximum value=k

Do it

A store sells T-shirts. It is known that the unit price when purchased in batches is 2.5 yuan. According to market research, the sales volume and unit price satisfy the following relationship: within a period of time, when the unit price is 13.5 yuan, the sales volume is 500 pieces, and the unit price is 13.5 yuan per unit. If you reduce the price by 1 yuan, you can sell 200 more pieces.

If the sales unit price is x yuan, (an integer of 20≤x≤35)

Price reduction ____________ yuan per piece

Sales volume can be represented by _______________ pieces

Profit per piece __________ yuan

Total profit obtained y =_________________________

The idea of ​​"quadratic function application"

Looking back at the process of solving the "maximum profit" and "maximum output" problems in this lesson, can you summarize the basic ideas for solving such problems?

1. Understand the problem;

2. Analyze the variables and constants in the problem and the relationship between them;

3. Express the relationship between them mathematically;

4. Do mathematical solutions;

5. Check the rationality and expansion of the test results, etc.

Class exercises

A travel agency organizes a group trip to other places. The minimum group size is 30 people, and the unit price per person is 800 yuan. The travel agency gives a discount to groups with more than 30 people, that is, for every additional person in the tour group, the unit price per person will be reduced by 10 yuan. When the number of people in a tour group is how many, the travel agency can obtain the maximum turnover?

Solution: Suppose there are x people in a tour group, and the travel agency’s turnover is y yuan. Then

y=〔800-10(30-x)〕·x

=-10x2+1100x

=-10(x-55)2+30250

∴When x=55, the maximum value of y=30250

Answer: When there are 55 people in a tour group, the travel agency can earn a maximum profit of 30,250 yuan.

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Update Time: 2024-11-18

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