The maximum problem is an important part of junior high school mathematics, and there are maximum problems in algebra and geometry. The final exam mainly has important geometric conclusions (such as the shortest line segment between two points, the sum of two sides of a triangle is greater than the third side, the difference between the two sides is less than the third side, the shortest vertical line segment, etc.). ) and the problem of finding the maximum by using the properties of linear function and quadratic function.

Maximum value problem of linear function

Typical example:

1(20 10 Shaanxi) A young garlic shoot production base enjoyed a bumper harvest, harvesting 200 tons of young garlic shoots. According to market research, it can be sold in wholesale, retail and cold storage, and sales can be carried out in these three ways. The planned price and cost per ton are as follows:

Sales method: wholesale and retail, refrigerated sales.

Price (RMB/ton) 3000 4500 5500

If all young garlic shoots are sold as planned after a period of time, the profit will be Y (yuan), young garlic shoots will be X (ton), and the retail sales will be 0/3 of the wholesale volume of 65438+.