By definition 1 agi = 1 ap + 1 sudo agi and according to your formula 1 ap = 1/2 agi, 1 sudo agi = 1/4 agi.
Now if we substitute ap and sudo agi with the agi values you gave them we get 1 agi = 1/2 agi + 1/4 agi -> 1 agi = 3/4 agi
1 agi = 3/4 agi is obviously not possible.