For the product to be maximum for a set of numbers, they need to be close to each other. Having a big range (difference between the largest and the smallest number) would mean that the product will be not be maximum. Take an example of 3 numbers with a mean of 5. The numbers could be

4,5,6 product = 120

3,5,7 product = 105

2,5,8 product = 80

1,5,9 product = 45

0,5,10 product = 0

So as the range increases, the product decreases. Using the same concept the numbers need to be around the mean

which makes the 7 distinct integers as 27,28,29,30,31,32,33

so the answer is 27*33 = 891

please note a*b > (a-x)*(b+x)