Sunshine Shopping Mall bought a commodity at the price of 30 per piece, and found that the daily sales volume of this commodity m (pieces) and the sales price of each piece M = 162-3x （1） Write the functional relationship between sales profit y and sales price x) (2) If shopping malls want to get the maximum sales profit every day, how much is the most cost-effective price for each commodity? How much is the maximum sales profit?

Sunshine Shopping Mall bought a commodity at the price of 30 per piece, and found that the daily sales volume of this commodity m (pieces) and the sales price of each piece M = 162-3x （1） Write the functional relationship between sales profit y and sales price x) (2) If shopping malls want to get the maximum sales profit every day, how much is the most cost-effective price for each commodity? How much is the maximum sales profit?

y=m(x-30)=(162-3x)(x-30)=-3x^2+252x-4800
The equation reaches the maximum when x = - 252 / (- 2 * 3) = 42
That is, the price of goods is 42
The maximum profit y = 492 can be obtained by substituting x = 42 into the function

A shopping mall bought a commodity at the price of 30 yuan per piece. In the trial sale, it was found that the daily sales volume of this commodity M pieces and the sales price X Yuan satisfy the linear function M = 162-3x, 30 ≤ x ≤ 54
【1】 Write out the functional relationship between the daily sales profit y and the sales price X of this commodity
【2】 If shopping malls want to get the maximum sales profit every day, what is the most appropriate price for each commodity and what is the maximum sales profit?

By solving the problem, we get that the sales profit of each product is (X-30) yuan, then the sales profit of M products is y = m (X-30). And ∵ M = 162-3x, ∵ y = (X-30) (162-3x), that is, y = - 3x2 + 252x-4860. ∵ X-30 ≥ 0, ∵ x ≥ 30. And ∵ m ≥ 0, ∵ 162-3x ≥ 0, that is, X ≤ 54. ∵ 30 ≤ x ≤ 54

The unit price of a commodity purchased by a store is 30 yuan. In the trial sale, it is found that the relationship between the daily sales volume P (pieces) and the sales price x (yuan) of this commodity is satisfied: P = 100-2x. If the store wants to make a profit of 200 yuan every day, how much should the price of each commodity be set? How many pieces of this product are sold every day?

Suppose that the selling price of each commodity should be set at x yuan, and P pieces of this commodity should be sold every day. According to the meaning of the title: (X-30) (100-2x) = 200, it is sorted out as follows: x2-80x + 1600 = 0, {(x-40) 2 = 0,} X1 = x2 = 40} P = 100-2x = 20; therefore, the selling price of each commodity should be set at 40 yuan, and 20 pieces of this commodity should be sold every day

A shopping mall bought a product at the price of 30 yuan per piece. In the trial sale, it was found that the daily sales volume of M pieces of this product met the sales price of X yuan per piece
Linear function M = 162-3x, 30

(1)Y=(X-30)(162-3X) (30