1. Let one digit be x and ten digits be y, and we can get the inequality.

0≤x≤9 ( 1)

1≤y≤9 (2)

It is also derived from known conditions

x+y= 10 (3)

2x+2 & lt； ( 1/2)y (4)

The solution of simultaneous (1)(2)(3)(4) is x= 1 and y=9, so this two-digit number is 19.

2. 1. It takes x hours to set up two factories, A and B, and treat garbage at the same time.

Then we can get (55+45)x=700 x=7 (hours) according to the known conditions.

In the factory, it takes y hours to dispose of garbage every day.

Then there is an inequality group 700≤55y (1).

550y≤7370(2)

The simultaneous solution of (1)(2) is y= 13 (hours).