(2)P =(x-40)( 1600-20x)=-20x？ +2400 x-64000 = 144000- 136000 = 8000 .

When x=-2400/(-20*2)=60,

Y has the maximum value =-20*60? +2400*60-64000= 144000- 136000=8000。

The solution is x 1=50, x2 = 70.

∵ The opening of parabola P=-20(x-60)2+8000 is downward,

When 50≤x≤70, the profit of selling zongzi every day is not less than 6000 yuan.

And ∵x≤58, ∴ when x=60, the maximum value of p =8000 yuan,

That is, when the price of each box is set as 60 yuan, the maximum profit is 8000 yuan;

(3)6000/(58-40)= 1000/3

The smallest integer greater than 1000/3 is 334.

That is, the supermarket sells at least 334 boxes of zongzi every day.