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A supermarket sells 2000 yuan refrigerators at 2400 yuan, an average of 8 refrigerators per day. In order to cooperate with the implementation of the national policy of "home appliances to the countryside", the supermarket The survey shows that if the price of this kind of refrigerator is reduced by 50 yuan, 4 more refrigerators will be sold every day. (1) suppose that the price of each refrigerator is reduced by X Yuan, and the profit of this kind of refrigerator is y yuan every day. Please write the function expression between Y and X; (it is not required to write the value range of the independent variable.) (2) In order to make a profit of 4800 yuan per day in the sales price of this kind of refrigerator, and at the same time make the people get benefits, how much should each refrigerator be reduced? Ask for a way to do this,
Solution (1): suppose that the price of each refrigerator is reduced by X Yuan, and the daily profit of this refrigerator is y yuan; then the average number of refrigerators sold is (4 × X / 50), and the actual average number of refrigerators sold is [8 + (4 × X / 50)], and the profit of each refrigerator is (2400-2000-x)
y=[8+(4×x/50)](2400-2000-x)
=(8+0.08x)(400-x)
=3200-8x+32x-0.08x²
=-0.08x²+24x+3200
y=-0.08x²+24x+3200
(2) If the market wants to make a profit of 4800 yuan per day in the selling price of this kind of refrigerator, y = 4800, there is an equation
-0.08x²+24x+3200=4800
0.08x²-24x+1600=0
x²-300x+20000=0
(x-100)(x-200)=0
X-100 = 0 or X-200 = 0
x1=100
x2=200
If we want to benefit the people, we should reduce the price more
So the solution is x = 200, each refrigerator should be reduced by 200 yuan
RELATED INFORMATIONS
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