The purchase price of a commodity is 30 yuan/piece, the current price is 40 yuan/piece, and it can be sold 150 pieces per week. Market research shows that if the price of each piece increases by 1 yuan (the price of each piece cannot be higher than that of 45 yuan), 10 pieces will be sold every week. Suppose the price of each piece goes up by X yuan (X is a non-negative integer), and the weekly sales volume is Y pieces. (2) How to set the price to maximize weekly profit and increase weekly sales? What is the maximum profit per week?

& lt 1 & gt； From the meaning of the question, y= 150- 10x, because the price of each piece cannot be higher than that of 45 yuan, so 45-40=5, (0=

& lt2> Let the total profit be W yuan, then W = (x+10) Y = (x+10) (150-10x) =-10x2+50x+.

Pay attention to the topic (Maximizing weekly profit and increasing weekly sales), two specific conditions, so x=2, so the price is 40+2=42, the weekly profit is the largest and the sales volume is larger, and the maximum profit is 65,438+0, 560 yuan (brought into the above analytical formula).