About selling calculators! 1、 Oriental specialty store specializes in selling calculators of a certain brand. The purchase price is 12 yuan / piece and the selling price is 20 yuan / piece. In order to promote sales, the specialty store decides to buy more than 10 calculators, and the selling price will be reduced by 0.10 yuan for each additional one (for example, if someone buys 20 calculators, the price can be reduced by 0.10 * (20-10) yuan, and the price can be 19 yuan / piece), but the minimum is 16 yuan / piece (1) How many at least can customers buy at the lowest price? (2) Write out the functional relationship between profit y (yuan) and purchase quantity x (pieces) when x pieces are purchased at one time (x > 10); (3) One day, a customer bought 46 and another customer bought 50. The exclusive store found that the profit of selling 50 was less than that of selling 46. In order to make more money each time, and other sales conditions remained unchanged, how much should the lowest price of 16 yuan be raised at least? Why?

About selling calculators! 1、 Oriental specialty store specializes in selling calculators of a certain brand. The purchase price is 12 yuan / piece and the selling price is 20 yuan / piece. In order to promote sales, the specialty store decides to buy more than 10 calculators, and the selling price will be reduced by 0.10 yuan for each additional one (for example, if someone buys 20 calculators, the price can be reduced by 0.10 * (20-10) yuan, and the price can be 19 yuan / piece), but the minimum is 16 yuan / piece (1) How many at least can customers buy at the lowest price? (2) Write out the functional relationship between profit y (yuan) and purchase quantity x (pieces) when x pieces are purchased at one time (x > 10); (3) One day, a customer bought 46 and another customer bought 50. The exclusive store found that the profit of selling 50 was less than that of selling 46. In order to make more money each time, and other sales conditions remained unchanged, how much should the lowest price of 16 yuan be raised at least? Why?

(1) At least buy x, according to 0.10 * (20-10) = 1, the solution is 0.10 * (X-10) = 4, x = 50
(2) Y1 = (20-12) x = 8x (x ≤ 10), y2 = [20 - (X-10) * 0.1] * X-12 * x = - 1 / 10x ^ 2 + 9x (10 ＜ x ≤ 50), Y3 = (16-12) x = 4x (x ＞ 50) when y = 180 is calculated according to y2 = - 1 / 10x ^ 2 + 9x, solving the equation, we get X1 = 30, X2 = 60 (rounding off), so the customer bought 30 calculators this time
(3) In fact, it is the maximum value of y2 = - 1 / 10x ^ 2 + 9x (10 < x ≤ 50). According to the maximum value of y when x = - B / 2a, x = 45,
Because other sales conditions remain unchanged, so
The lowest price is = 20 - (X-10) 0.1 = 20 - (45-10) * 0.1 = 16.5
So each one should be raised to at least 16.5 yuan