The box has X pieces of cardboard and the bottom cover has Y pieces.

Option 1:

2x:3y= 1:2

x+y=20

Solution: X = 60/7 is about 8. Duo, and y is about 1 1. A duo.

If x is 8, y is 12. There are 16 boxes and 36 bottom covers.

You can make 16 boxes.

If x is 9 and y is 1 1, there are 18 boxes and 33 bottom covers.

Only 16 boxes can be made.

Option 2:

(2x+ 1):(3y+ 1)= 1:2

x+y= 19

Solution: x = 8, y = 1 1.

There are 17 boxes and 34 bottom covers.

You can make 17 boxes.

To sum up, scheme 2 is better.