Nanbo Automobile City sells a certain type of car, and the purchase price of each car is 250,000. Market research shows that when the sales price is 290,000 yuan, eight cars can be sold every week on average, and when the sales price is not reduced by 5,000 yuan, four more cars can be sold every week on average. If the price of each car is reduced by X million yuan, the sales profit of each car is Y million yuan (sales profit = sales price-purchase price).

(1) Find the functional relationship between Y and X, and write the value range of X on the premise of ensuring that the merchant does not lose money.

(2) Assuming that the average weekly sales profit of this kind of car is Z ten thousand yuan, try to write the functional relationship between Z and X..

(3) When the price of each car is tens of thousands of yuan, the average weekly sales profit is the largest? What is the maximum profit?

(1) The original profit of each vehicle is: 29-25 = 40,000 yuan.

Now the profit of each car is: Y=4-X, (0

(2)z=(29-25-x)[8+(x/0.5)*4]=(4-x)(8+2x)=32+8x-8x-2x^2=32-2x^2

(3)Z=-2x^2+32

So when X=0, z takes the maximum value, which is 32.

That is, when the price is 290,000 yuan, the maximum profit is 320,000 yuan, which can be used for reference.