A store bought a batch of daily necessities with a unit price of 16 yuan. After selling for a period of time, in order to obtain more profits, the store decided to increase the selling price. According to the test, if the price is 20 yuan per piece, 360 pieces can be sold per month; if the price is 25 yuan per piece, 210 pieces can be sold per month. Suppose that the number of pieces sold per month y (pieces) is a function of the price x (yuan / piece). (1) ）Try to find the relationship between Y and X; (2) under the condition that there is no overstock of goods and other factors are not considered, how much is the selling price to make the maximum profit every month? What is the maximum monthly profit (total profit = total revenue - total cost)?

A store bought a batch of daily necessities with a unit price of 16 yuan. After selling for a period of time, in order to obtain more profits, the store decided to increase the selling price. According to the test, if the price is 20 yuan per piece, 360 pieces can be sold per month; if the price is 25 yuan per piece, 210 pieces can be sold per month. Suppose that the number of pieces sold per month y (pieces) is a function of the price x (yuan / piece). (1) ）Try to find the relationship between Y and X; (2) under the condition that there is no overstock of goods and other factors are not considered, how much is the selling price to make the maximum profit every month? What is the maximum monthly profit (total profit = total revenue - total cost)?

(1) Let y = KX + B, then there is 360 = 20K + b210 = 25K + B. the solution is k = - 30b = 960  y = - 30x + 960 (16 ≤ x ≤ 32) (4 points) (2) monthly profit P = (- 30x + 960) (x-16) = 30 (- x + 32) (x-16) (5 points) = 30 (- x2 + 48x-512) = - 30 (x-24) 2 + 1920 (7