You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to search and python interpreter tool to calculate the math problem for fact information about specific topics if needed. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags respectively, and the search query and result are enclosed within <search> </search> and <result> </result> tags respectively. For example, <think> This is the reasoning process. </think> <search> search query here </search> <result> search result here </result> <think> This is the reasoning process. </think> <python> python code here </python> <result> python interpreter result here </result> <think> This is the reasoning process. </think> <answer> The final answer is \[ oxed{answer here} \] </answer>. In the last part of the answer, the final exact answer is enclosed within oxed{} with latex format.
system
The cost price of a certain product is 40 yuan per item. When the selling price is set at 60 yuan per item, 300 items can be sold per week. Now, it is necessary to reduce the price, and according to market research: for every 1 yuan reduction in price, 20 more items can be sold each week. Under the premise of ensuring profit, solve the following questions:  
(1) If the price is reduced by x yuan per item and the weekly profit from selling the goods is y yuan, please write the function relationship between y and x, and find the range of values for the independent variable x;  
(2) If the minimum unit of price reduction is 1 yuan, how much should the price be reduced to maximize the weekly profit? What is the maximum profit?
user
6125
rule
The cost price of a certain product is 40 yuan per item. When the selling price is set at 60 yuan per item, 300 items can be sold per week. Now, it is necessary to reduce the price, and according to market research: for every 1 yuan reduction in price, 20 more items can be sold each week. Under the premise of ensuring profit, solve the following questions:  
(1) If the price is reduced by x yuan per item and the weekly profit from selling the goods is y yuan, please write the function relationship between y and x, and find the range of values for the independent variable x;  
(2) If the minimum unit of price reduction is 1 yuan, how much should the price be reduced to maximize the weekly profit? What is the maximum profit?
train