1. If the purchase price is x and the purchase price is y, the equations are: x-45=y, (0.85x-y)*8=(x-35-y)* 12.

Based on the above two formulas, x= 200 y= 155 is obtained, so the purchase price of each eye lamp is 155, and the bid price is 200.

2. If the price is reduced by one yuan, you can sell four more units,1* * (100+4a), and the price of each unit is: (200-a).

So the income of each set is: (200- 155-a)=(45-a) yuan.

Then the daily profit W=( 100+4a)*(45-a), which is a function of the daily profit of Xinhua Shopping Mall.

3. w = (100+4a) * (45-a) =-4a2+80a+4500, and the maximum value can be obtained.